What will be the percentage increase in the area of the triangle if each side of the triangle is doubled? [4 MARKS]

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Solution

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

Let a, b, c be the sides of the triangle.

$S_{1} = \frac{P e r i m e t e r}{2}$ = $\frac{a + b + c}{2}$

Area of the triangle $(A_{1}) = \sqrt{s (s - a) (s - b) (s - c)}$

Now the sides are doubled

$S_{2} = \frac{P e r i m e t e r}{2}$ = $\frac{a + b + c}{2} = 2 S_{1}$

Area of the triangle= $\sqrt{s (s - a) (s - b) (s - c)}$

= $\sqrt{2 S_{1} (2 S_{1} - 2 a) (2 S_{1} - 2 b) (2 S_{1} - 2 c)}$

= $4 \sqrt{s (s - a) (s - b) (s - c)} = 4 A_{1}$

Therefore percentage increase = $\frac{4 A_{1} - A_{1}}{A_{1}}$ × 100 = 300%.

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