Question

A rectangle with sides 12 cm and 14 cm has the same diagonal as a square.
What is the length of the side of the square.
Give your answer as a surd.

Answer 1

$\sf \: side \: of \: rectangle \: = 12cm \: and \: 14cm$

$\sf \: let \: \red{x} \: be \: diagonal \: of \: rectangle \:$

$\sf \green{Pythagoras \: theorem : } {The\: square \:of \:hypothesised is \:equal \:to\: sum \:of \:square of \:side .}$

$\sf \: here \: hypotenuse \: = \red{x}$

$\tt \implies {x}^{2} = {12}^{2} + {14}^{2}$

$\implies \tt \: {x}^{2} = 144 + 196$

$\implies \tt {x}^{2} = 340$

$\implies \tt \boxed{x = \sqrt{340} }$

$\sf \: diagonal \: of \: square \: = \red{ \sqrt{340} }$

$\sf \: let \: side \: square \: = \red{a}$

$\sf \green{A gain \: use \: Pythagorean \: theorem \: }$

$\tt\implies340 = {a}^{2} + {a}^{a}$

$\implies \tt2 {a}^{2} = 340$

$\implies \tt {a}^{2} = \frac{ \cancel{340}}{ \cancel{2}}$

$\implies \tt {a}^{2} = 170$

$\boxed{\implies \tt \: a = \sqrt{170} }$