Question

Find the percentage increase in the area of a triangle if it's each side is doubled using heron 's formula.

Answer 1

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

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

S1=Perimeter2 = a+b+c2

Area of the triangle (A1)=√s(s−a)(s−b)(s−c)

Now the sides are doubled

S2=Perimeter2 = a+b+c2=2S1

Area of the triangle= √s(s−a)(s−b)(s−c)

= √2S1(2S1−2a)(2S1−2b)(2S1−2c)

= 4√s(s−a)(s−b)(s−c)=4A1

Therefore percentage increase = 4A1−A1A1 × 100 = 300%.