Question

The difference between the sides at right angle in a right angle triangle is 14cm. The area of a triangle is 120cmsquare. Calculate the perimeter of the triangle.

Answer 1

Answer:

perimeter = 60cm

Step-by-step explanation:

area of right angle triangle = 1/2 × b × h = 120

let base = x height = y

x - y = 14

x = 14 + y

area = 120

$120 = \frac{1}{2} \times x \times y \\ 120 = \frac{1}{2} \times (14 + y) \times y \\ 240 = {y}^{2} + 14y \\ {y}^{2} + 14y - 240 = 0 \\ {y}^{2} - 10y + 24y - 240 = 0 \\ y(y - 10) + 24(y - 10) = 0 \\ (y - 10)(y + 24) = 0 \\ y - 10 = 0 \: \: \: \: \: \: \: \: y + 24 = 0 \\ y = 10 \: \: \: \: \: y = - 24$

we take the positive value of y

x = y+14= 10+14= 24

by Pythagoras theorem

${hyp}^{2} = {opp}^{2} + {adj}^{2} \\ = {24}^{2} + {10}^{2} \\ = 576 + 100 \\ = 676 \\ hyp \: = \sqrt{676} = 26$

perimeter of triangle is

26 + 24 + 10 = 60cm