Find below the NCERT Exemplar problems and their solutions for Class 10 Mathematics Chapter, Triangles:

Exercise 6.4

Long Answer Type Questions (Q. NO. 7-12):

Question. 7 A flag pole 18m high casts a shadow 9.6m long. Find the distance of the top of the pole from the far end of the shadow.

Solution.          

Let BC = 18m be the flag pole and AB be its shadow which is 9.6m long.

Question. 8 A street light bulb is fixed on a pole 6m above the level of the street. If a woman of height 1.5m casts a shadow of 3m, then find how far she is away from the base of the pole.

Solution.

Let the bulb be fixed at top A of pole AB and CD = 1.5m be the height of a woman and ED = 3m be the length of her shadow.

Hence, the required distance between base of pole and woman is 9m.

Question. 9 In given figure, ABC is a triangle right angled at B and BD ⏊ AC. If AD = 4cm and CD = 5cm, then find BD and AB.

Question. 10 In given figure PQR is a right triangle, right angled at Q and QS ^ PR. If PQ = 6cm and PS = 4cm, then find QS, RS and QR.

Question. 11 In DPQR, PD ^QR such that D Lies on QR, if PQ = a, PR = b, QD = c and DR = d, then prove that (a + b)(a  − b) = (c + d) (c − d).

Solution.        

Hence proved.

Question. 12   In a quadrilateral ABCD, ÐA + ÐD = 90°. Prove that\

                                    AC² + BD² = AD² + BC².

Solution.        

Given: In quadrilateral ABCD, ÐA + ÐD = 90°

To prove: AC² + BD² = AD² + BC²

Construct: Produce AB and CD to meet at E.

Also, join AC and BD.