Mensuration Practice Test 4

Area of the isosceles triangle = 192 cm
Area = $\frac{\mathit{b}}{4}\sqrt{4{\mathit{a}}^2-{\mathit{b}}^2}$
192 = $\frac{24}{4}\sqrt{4{\mathit{a}}^2-{\left(24\right)}^2}$
192 = $6\sqrt{4{\mathit{a}}^2-576}$
$\frac{192}{6}$ = $\sqrt{4{\mathit{a}}^2-576}$

32 = $\sqrt{4{\mathit{a}}^2-576}$
1,024 = $4{\mathit{a}}^2$ − 576
1,600 = $4{\mathit{a}}^2$
${\mathit{a}}^2$ = 400
a = 20 cm.
Perimeter of the triangle = 2a + b = 2 (20) + 24
= 40 + 24
= 64 cm.