Question

Need some help with this. It says to find x.

Answer 1

Explanation:

3x = 15

3x/3 = 15/3

x = 5

3(5) = 15

Answer 2

x= 5

Explanation:

Since RQ= PQ,

3x= 15

Divide both sides by 3:

x= 15 ÷3

`\textcolor{red}{x = 5}`

`\textcolor{steelblue}{\text{Prove for RQ}= \text{PQ}}`

Let SP= x

RS= SP= x (given)

Let SQ= y

Applying Pythagoras' Theorem,

In triangle QRS

(RQ)²= (RS)² +(SQ)²

(RQ)²= x² +y²

`RQ = \sqrt{ {x}^(2) + {y}^(2) }`

In triangle QPS

(PQ)²= (SP)² +(SQ)²

(PQ)²= x² +y²

`PQ = \sqrt{ {x}^(2) + {y}^(2) }`

Thus, RQ= PQ.