Mathematics
PQR is a triangle. S is a point on the side QR of △PQR such that ∠PSR = ∠QPR. Given QP = 8 cm, PR = 6 cm and SR = 3 cm. (i) Prove △PQR ~ △SPR. (ii) Find the lengths of QR and PS. (iii) area of △PQR/area of △SPR
Related Questions
In the given figure, ABC is a right angled triangle with ∠BAC = 90°.
(i) Prove that : △ADB ~ △CDA.
(ii) If BD = 18 cm and CD = 8 cm, find AD.
(iii) Find the ratio of the area of △ADB is to area of △CDA.
ABC is a right angled triangle with ∠ABC = 90°. D is any point on AB and DE is perpendicular to AC. Prove that :
(i) △ADE ~ △ACB
(ii) If AC = 13 cm, BC = 5 cm and AE = 4 cm. Find DE and AD.
(iii) Find, area of △ADE : area of quadrilateral BCED.
Rohan is trying to find the height of a tower shown below. He is using the properties of similar triangles. He observes a lamp post near it of height 5 m casting a shadow of 4 m on the ground. At the same time, he himself is casting a shadow of 1 m on the ground.
Based on the above information, answer the following questions :
(i) What is the height of the tower ?
(ii) What is Rohan's height ?
(iii) What will be the length of the shadow of the lamp post when the tower casts a shadow of 35 m ?
