Question

The area of
triangle is 84 cm. If
the length of the
sides
are
consecutive natural
numbers, then what
are the dimensions
(in cm) of the
triangle?​

Answer 1

Explanation:

Perimeter of the triangle = 84 cm.

One side = 30 cm.

The sum of the other two sides = 84–30 = 54 cm

Let the other two sides be x cm and (54-x) cm.

By Heron’s formula: 336 = [42*12*(42-x)*(42–54+x)]^0.5

112896 = [42*12*(42-x)*(42–54+x)], or

224 = (42-x)*(x-12) = 42x-x^2–504+12x, or

x^2^ - 54x +728 = 0

x = [54+(2916–2912)^0.5]/2

= [54+2}/2

= 28 cm.

The other two sides are 28 cm and 26 cm. Answer.