# CASE STUDY QUESTION 17-Class X-Maths

CASE STUDY QUESTION 17-Class X-Maths

**On one day, a poor girl of height 90 cm is looking for a lamp-post for completing her homework as in her area power is not there and she finds the same at some distance away from her home. After completing the homework, she is walking away from the base of a lamp-post at a speed of 1.2 m/s. The lamp is 3.6 m above the ground (see below figure).**

**(i) Find her distance from the base of the lamp post.**

(a) 1.2 m (b) 3.6 m (c) 4.8 m (d) none of these

Let AB denote the lamp-post and CD the girl after walking for 4 seconds away from the lamp-post.

From the figure, DE is the shadow of the girl.

Let DE be x metres.

Now, her distance from the base of the lamp =

BD = 1.2 m × 4 = **4.8 m.**

**(ii) Find the correct similarity criteria applicable for triangles ABE and CDE.**

(a) AA (b) SAS (c) SSS (d) AAS

**(iii) Find the length of her shadow after 4 seconds.**

(a) 1.2 m (b) 3.6 m (c) 4.8 m (d) none of these

**(iv) Sides of two similar triangles are in the ratio 9:16. Find the ratio of Corresponding areas of these triangles.**

(a) 9:16 (b) 3:4 (c) 81:256 (d) 18:32

Since ratio of the areas of two similar triangles is equal to the ratio of the square of their corresponding sides,

Ratio of areas of similar triangles = √9 : √16 = 3 : 4

**(v) Find the ratio AC:CE.**

(a) 1: 3 (b) 3 : 1 (c) 1 : 4 (d) 4 : 1