Question

EXAMPLE 11 Find the percentage increase in the area of a triangle if its each side is doubled.
SOLUTION Let a, b, c be the sides of the old triangle and sbeits semi-perimeter. Then,​

Answer 1

Answer:

300%

Explanation:

Using Heron's formula

let sides of triangle A = a, b,  c and of tringle B = 2a , 2b , 2c

s = a+b+c/2 , 2s = a+b+c          s' = 2a + 2b + 2c/2 = a+b+c

When each side is doubled, the new sides are 2a,2b,2c.

s' = 2s

area of A = √s(s-a)(s-b)(s-c)

area of B =√ 2s(2s-2a)(2s-2b)(2s-2c) = 4 √s(s-a)(s-b)(s-c)

increase in area = 3 √ s(s-a)(s-b)(s-c)

percentage increase = 3 x 100 = 300%

Hope it helps!...

Answer 2

Answer:

300%

Step-by-step explanation:

s= a+b+c/2

after each side doubles

s1 = 2(a+b+c)/2 = 2s

area after each side double = A1

= sqrt(2s×(2s-2a)×(2s-2b)×(2s-2c))

=4 ×area

when each side of triangle gets doubled area increases by 4 times

let area be A

A' - A 4A -A

% increase in area = _____ = ______×100

A A

=300%