Mensuration Practice Test 10

Let the sides of the triangle be 5x, 12x and 13x.
So, perimeter ⇒ 5x +12x +13x = 60
x = 2
So, side of triangle = 10, 24 and 26
Area of Triangle = $\sqrt{\mathit{S}\left(\mathit{s}-\mathit{a}\right)\left(\mathit{s}-\mathit{b}\right)\left(\mathit{s}-\mathit{c}\right)}$
S = $\frac{\mathit{a}+\mathit{b}+\mathit{c}}{2}$ = $\frac{10+24+26}{2}$ = 30
Area of triangle = $\sqrt{30\left(30-10\right)\left(30-24\right)\left(30-26\right)}$
= $\sqrt{30\times 20\times 6\times 4}$
= $\sqrt{14400}$
= 120 cm
Volume of the prism = (Area of base) × Height
= 120 × 50 = 6,000 $\mathit{c}{\mathit{m}}^3$