Math, asked by devesh5113, 1 year ago

the difference of length of sides forming right angle triangle is 3 CM if the perimeter of the triangle is 36 cm find the area of the triangle​

Answers

Answered by DayDreamer2943
45
let the perpendicular height be X

let the base of the triangle be X + 3

by Pythagoras theorem,

hypo \: = {x}^{2} + ({x + 3})^{2}

hypo \: = {2x}^{2} + 6x + 9

As the perimeter of the triangle is 36 cm,

36 = {2x}^{2} + 6x + 9 + x + x + 3

36 = {2x}^{2} + 8x + 12

 {2x}^{2} + 8x - 24 = 0

 {x}^{2} + 4x - 12

x(x + 6) \: - 2(x + 6) =

(x - 2)(x + 6) = 0

x = 2 \: or \: - 6
Rejecting -6,
x = 2cm

The perpendicular = 2cm
The base = 5cm

The area of the triangle = 1/2×5×2

= 5 cm sq.

devesh5113: answer given at back is 54
Similar questions