CBSE Class 10 Mathematics Triangles Worksheet Set E

Triangles

Q.- In figure, ∠CAB = 90º and AD ⊥ BC. If AC = 75 cm, AB = 1 m and BD = 1.25 m,find AD.

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More question-

1. What value of x will make DE II AB in the given figure? C

X - 2 x - 1 (x =4)

D E

X x + 2

A B

2. In figure, DE is parallel to base BC. If AD = 2.5 cm, BD = 3.0 cm and AE = 3.75 cm, find the length of AC

A

2.5cm 3.75cm

D E

3.0 cm (8.25cm)

B C

3. In the figure. XY II BC . Find the length of XY A

1cm

X Y (2cm)

2cm

B C

6cm

4. In figure, considering triangles BEP and CDP, prove that:

BP X PD = EP X PC A

E D

P P

B C

5 .D is a point on the side BC of a ΔABC such that angle ADC = angle BAC. Prove that CA ∕∕ CD = CB ∕∕ CA

6. In figure angle ACB = 90• , CD perpendicular to AB, prove that CD2 = BD . CD

C

A D B

7. A vertical pole which is 2.25m long casts a 6.75m long shadow on the ground. At the same time a vertical Tower casts a 90m long shadow on the ground. Find the height of the tower (30m)

8. If Δ ABC ~ Δ PQR. Also ar (ΔABC) = 4 ar (Δ PQR). If BC = 12cm, find QR (6cm)

9. The areas two similar triangles ABC and DEF are 36 cm2 and 81 cm2 respectively. If EF = 6.9 cm, determine BC (4.6 cm)

10. Two isosceles triangles have equal angles and their areas are in the ratio 81: 25. Find the ratio of their Corresponding heights

11. D, E and F are respectively the mid points of the sides BC, CA and AB of ΔABC. Find the ratio of the areas of Δ DEF and Δ ABC (1 : 4)

12. The perimeters of two similar triangles are 36cm and 48cm respectively. If one side of the first triangle is 9cm, what is the corresponding side of the other triangle (12cm)

13. In triangle ABC, AB= √3a, AC = a and BC = 2a. Prove that ∟A = 90˚

14. In triangle ABC, ∟BAC = 90˚ and AD ┴ BC. If BD = 8cm, DC= 18 cm, find AD

15. Two poles of height 8m and 13m stand on a plane ground. If the distance between their tips is 13m, find the distance between their feet (12m)

16.Two poles of height 10m and 15m stand vertically on a plane ground. If the distance between their feet is 5√3m, find the distance between their tops (10m)

17. The perpendicular from A on side BC of a triangle ABC intersects BC at D such that BD = 3CD. Prove

Please click the below link to access CBSE Class 10 Mathematics Triangles Worksheet Set E