Question

The sides of a triangular plot are in the ratio of 16: 8 : 10 and its perimeter is 340 m. Find its area in $m^2$ [4 MARKS]

Answer 1

Concept : 1 Mark
Application : 1 Mark
Calculation : 2 Marks

Suppose that the sides, in metres, are 16x, 8x and 10x.

Then, we know that 16x + 8x + 10x = 340 (perimeter of the triangle)

Therefore, 34x = 340, which gives x = 10.

So the sides of the triangle are
16× 10 m = 160 m, 8 × 10 m = 80 m and 10 × 10 m = 100 m.

We have s = $\frac{(160+100+80)}{2}$

s = 170 m,

and area will be $\sqrt{170(170-160)(170-100)(170-80)}$ $m^2$

= 100$\sqrt{1071}$ $m^2$