Mensuration Practice Test 8

Perimeter of the triangle = 32 cm
A = 11 cm
B = x
C = x − 5 cm.
A + B + C = 32
11 + x + x − 5 = 32
6 + 2x = 32
2x = 26
x = 13
B = 13 cm
C = x − 5 = 8 cm.

Area of the triangle = S = $\frac{\mathit{a}+\mathit{b}+\mathit{c}}{2}$ = $\frac{32}{2}$ = 16
A = $\sqrt{\mathit{s}\left(\mathit{s}-\mathit{a}\right)\left(\mathit{s}-\mathit{b}\right)\left(\mathit{s}-\mathit{c}\right)}$
= $\sqrt{16\left(16-11\right)\left(16-13\right)\left(16-8\right)}$
= $\sqrt{16\times 5\times 3\times 8}$
= $8\sqrt{30}\mathit{c}{\mathit{m}}^2$