Question

In triangle ABC;angle a=90°, sideAB= x cm, AC= (x+5)cm and area = 150 square metre. Find the sides of the triangle

Answer 1

Given that angle A is 90°

So AB = height = x cm

AC = base = x+5 cm

Area = 150 cm^2

it is wrong

=> 1/2 × base × height = 150

=> 1/2 × (x+5) × x = 150

=> x(x+5) = 2×150 =300

=> x^2 + 5x - 300 = 0

=> x^2 + 20x -15x - 300 = 0

=> x(x+20) - 15(x+20) = 0

=> (x+20)(x-15)= 0

=> x = 15 or -20

Since length can not be negative, x = 15 cm

height = x = 15cm

base = x+5 = 15+5 = 20 cm

hypotenuse = √(15^2 + 20^2) = √625 = 25cm

Sides of triangle are 15cm, 20cm and 25cm.

Answer 2

Given that angle A is 90°

So AB = height = x cm
AC = base = x+5 cm

Area = 150 cm^2
(you have wrongly mentioned it as m^2)

=> 1/2 × base × height = 150

=> 1/2 × (x+5) × x = 150

=> x(x+5) = 2×150 =300

=> x^2 + 5x - 300 = 0

=> x^2 + 20x -15x - 300 = 0

=> x(x+20) - 15(x+20) = 0

=> (x+20)(x-15)= 0

=> x = 15 or -20

Since length can not be negative, x = 15 cm


height = x = 15cm

base = x+5 = 15+5 = 20 cm

hypotenuse = √(15^2 + 20^2) = √625 = 25cm


Sides of triangle are 15cm, 20cm and 25cm.