1. Two sides of a triangle are 0.5 cm and 3cm. The third side of the triangle is of integral units. A median is drawn from the common point of side 0.5 cm and 3 cm to the third side. Find the length of the median.
2. If a triangle ABC has area of 48 square units, and BE and AD are two medians to sides AC and BC respectively. The two medians intersect at point G, can you find the ratio of areas of triangles AGE and BGD.
3. If in the triangle PQR, medians PT and QS intersect at O. If the length of PT = 21 units and QS = 15 units, find the length of PO and OS.
4. If in the triangle PQR, medians PT and QS intersect at O. If the length of OT is 8 units and OQ is 12 units, find the length of medians PT and QS.
5. In a triangle ABC, AD is the angle bisector, then find the ratio of BD : DC if AB = 15 units and AC = 12 units.
6. In a triangle ABC, bisectors of angle B and C intersect at point I inside the triangle. Find the measure of angle BIC, if angle BAC is given as 50 degrees.
7. In a triangle ABC, bisectors of angle A and C intersect at point I inside the triangle. Find the measure of angle ABC, if angle AIC is given as 120 degrees.
8. In a triangle ABC, AD, BE and CF are the angle bisectors of angle A, B and C respectively. If AB = 5 cm, BC = 8 cm and CA = 4 cm, find the lengths of AF, CE and BD.
1. In a right-angled triangle ABC (with B being 90 degrees), DE is drawn parallel to BC. Area of triangle ADE is 36 square units, while area of quadrilateral DEBC is 45 square units, find the ratio AD : AB and AD : DB.
2. In right angle triangle QPR (with P being 90 degrees), PS is drawn perpendicular on QR, if the length of QR = 25 units, PR = 20 units, find the lengths of PQ, QS and SR.
3. In a right-angled triangle ABC (with B being 90 degrees), a square DEBF is drawn with points D and F on AB and BC respectively. If the length of sides of triangle ABC is AB = 12, BC = 16 and AC = 20 units, can you find the length of side of square DEBF?
4. In a right-angled triangle ABC (with B being 90 degrees), point P and Q is taken on AC and CB respectively such that angle QPC is 90 degrees. If the length of BC = 12 units, AB = 9 units and PQ = 6 units. Find the length of CQ, BQ and PC.
5. In a right-angled triangle ABC (with B being 90 degrees), point P and Q is taken on AC and CB respectively such that angle QPC is 90 degrees. If the length of BC = 12 units, AB = 9 units and PQ = 6 units.
a) Find the ratio of area of triangle ABC and QPC.
b) Find the ratio of area of triangle QPC and quadrilateral QPAB.
6. A vertical stick 12 cm long casts a shadow 8 cm long on the ground. At the same time, a tower casts a shadow 40 cm long on the ground, determine the height of the tower.
7. In a right-angled triangle BAC, (angle A being 90 degrees), DEFG is a square drawn with points D, E, G and F lying on sides BC, BC, AB and AC respectively. If AB = 16, AC = 12 and BC = 20 units, find the length of the side of square DEFG.
8. ABCD is a square, F is the mid-point of AB and BE is one-third of BC. If the area of triangle FBE is 108 square units, find the length of AC.
1. If the area of two similar triangles ABC and PQR is given as 196 square units and 100 square units respectively. If the length of AB is 7 units, find the length of PQ.
2. If the lengths of sides AB and PQ of similar triangles ABC and PQR is given as 10 units and 15 units respectively, find the area of triangle PQR, if area of triangle ABC is given as 120 square units.
3. In triangle ABC, a line DE is drawn parallel to BC with points D and E on the sides AB and AC respectively. If the length of DE is given as 5 units and BC is 7 units, find the ratio of the area of triangle ADE : area of quadrilateral DEBC.
4. In triangle ABC, a line DE is drawn parallel to BC with points D and E on the sides AB and AC respectively. If the length of DE is given as 5 units and BC is 7 units, find the ratio of the altitudes of two similar triangles ADE and ABC.
5. In triangle ABC, a line DE is drawn parallel to BC with points D and E on the sides AB and AC respectively. If the length of AD is given as 5 units and DB is 3 units,
a) find the ratio of areas of triangles ADE and ABC.
b) find the ratio of areas of triangle ADE : area of quadrilateral DEBC.
6. In triangle ABC, a line CD is drawn from vertex C meeting side AB at D. If angle DCB is equal to angle BAC, then identify a pair of similar triangles in the figure.(Give reasons)
7. Find the in-radius and circumradius of a right-angle triangle having dimensions 9, 12 and 15 units.
8. In a right-angled triangle PQR (with Q being 90 degrees), QT is drawn perpendicular on PR. if the length of PQ = 16 units, QR = 12 units, find the length of QT, PT and TR.
9. In a trapezium, AB and DC are parallel sides with length 12 and 7 units. If the two diagonals AC and BD of trapezium ABCD intersect at O, find the ratio of areas of triangles AOB and DOC.
Also, can you guess the ratios of areas of triangles AOD and BOC?
10. In a paralleogram ABCD, AP : PB = 4 : 3, DQ : QC = 5 : 2. AQ and DP intersect at O.
a) Can you identify a pair of similar triangles? (Give reasons)
b) If yes, then find the ratio of areas of triangles AOP and DOQ?
11. In a triangle ABC, AE is a median drawn on side BC. G is the centroid on the line AE such that GH is perpendicular to BC, also AD is drawn perpendicular on BC. If the length of AD is given as 30 units, find the length of GH.
Answer key
5 2. 270 3. 25:24 4. 5 : 7 5. A) 25:64 5. B) 25 : 39
6. Triangle ABC similar to triangle CBD 7. 3, 7.5 8. 9.6, 12.8, 7.2
9. 144 : 49, both have equal areas. 10. A) Triangle AOP similar to triangle QOD.
10am: Algebra (Continued)
3pm: Ratio (New Module)
Students who have done all the maths modules ,need to solve the respective assignments of those modules .Please make sure that you are done with all the posts of “Reading Skills Small Lessons ” .
All the students have to research and submit answers to these questions by Thursday. No copy paste, please. And it’s mandatory for all the students.
1. What do you know about Pakistan ?(Explain in terms of Population, Size, Its birth in 1947, Current India-Pakistan relationship, Role of Religion in society and more)
2. 1965 and 1971 India-Pakistan Wars ????????
3. Nawaz Sharif and recently concluded general Elections in Pakistan??????
12pm: Percentages (New Module from “Tuesday“) {Students willing to revise this module can also attend as Percentages concepts are used in DI module and other topics of Arithmetic)
3pm: Time Speed Distance (New Module from Monday) {Only for those who have done Ratio and Percentages Module}
7pm: Geometry (Continued)
Vocabulary Module will be from Tuesday, 21st May in two different time slots , 3pm and 5pm. All the students have to compulsorily attend this module in any one time-slot.
Ratios are just comparisons-comparing the sizes ,the numbers ,the quantum of any two or more comparable quantities .
Click on the image to launch the slide show. Each slide focuses on one simple idea at a time . Going through this is extremely important for later lessons , repeat till we are speaking in the same language .
Practice Questions:
1. Two friends separated by a certain distance start walking towards each other .When they meet one of them has walked 20 meters more than the other.If the ratio of the distances that each has covered is 2:3 ,find the distance that originally separated them .
2. If (7x-4y) : (3x +y) is 5:13 ,find the ratio of x and y .
3. If a:b is 2:3 ,b:c is 4:5 and c:d is 6:7 ,find the ratio of a:b:c:d
4. If 3A=4B=5C=6D and A+B+C+D = 1026 ,find the values of A,B,C, D .
5. If (a+b) : (b+c) : (c+a) is 3:4:5 and a+b+c = 18 ,find the value of a x b x c.
