Mensuration Practice Test 2

Perimeter of the right-angled triangle = 234
Hypotenuse = 97 m
By Pythagoras theorem,
$\left({\mathit{c}}^2\right)$ = ${\mathit{a}}^2+{\mathit{b}}^2$
${\left(97\right)}^2$ = $\left({\mathit{a}}^2\right)+{\left(137-\mathit{a}\right)}^2$
9409 = ${\mathit{a}}^2+18796+{\mathit{a}}^2-274\mathit{a}$
$2{\mathit{a}}^2-274\mathit{a}+9360$ = 0
${\mathit{a}}^2-137\mathit{a}+4680$ = 0
${\mathit{a}}^2-72\mathit{a}-65\mathit{a}+4680$ = 0
a(a − 72)− 65(a − 72) = 0
a = 65a = 72
a = 65
b = 137 − a
= 137 −65 = 72