Question

In figure, if triangle ROQ ~ triangle POS, then the value of OS is (A) 5.25 cm (B) 6.25 cm (C) 7.25 cm (D) 4.25 cm​

Answer 1

Option A: 5.25 cm

Explanation:

It is given that triangle ROQ is similar to triangle POS with measurements of:

RQ = 3

PS = 4.5

OR = 3.5

OQ = 3.5

Also, we know that if two triangles are similar, the sides of those two triangles are in proportion meaning that:

RQ/PS = OQ/OS = OR/OP

Let us consider RQ/PS = OQ/OS.

3/4.5 = 3.5/OS

3OS = 3.5 x 4.5

3OS = 15.75

OS = 15.75/3

OS = 5.25 --- Option A

Therefore the correct answer is option A: 5.25.

Answer 2

EXPLANATION.

As Both the Triangles are in Proportion,

RQ/PS = OQ/OS

➱ 3/4.5 = 3.5/OS

➱ OS = 3.5 x 1.5

➱ OS = 5.25cm

option A ⋙ 5.25cm is correct