Question

please answer this....with explanation ^_^
Thanks in advance♡​

Answer 1

Step-by-step explanation:

Perimeter is PQ+QR+RS+ST+TP

PQ=3

QR=4

ST=x

PT=x+1

Only side required is RS

Given PQR is Right angled triangle Right angle at Q.

As per Pythagoras theorem,

PR²=PQ²+QR²

PR²=3²+4²

PR²=25

PR=5 units

Given PST is Right angled triangle Right angle at S.

As per Pythagoras theorem,

PT²=PS²+ST²

(x+1)²=PS²+x²

PS²=(x+1)²-x²

PS²= x²+2x+1-x²

PS=

$\sqrt[2]{2x + 1 \\ }$

Given PRS is Right angled triangle Right angle at R.

As per Pythagoras theorem,

PS²=PR²+SR²

2x+1=25+SR²

SR²=2x+1-25