Question

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

Answer 1

Answer:

3x = 15

x = 5

Step-by-step explanation:

Answer 2

Answer:

x= 5

Step-by-step 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.