Question

The sides forming the right angles and a hypotenuse of a right angled triangle are x cm ,(2x+2)cm and (3x-2)cm. Calculate the lengths of the sides of the triangle​

Answer 1

let a and b be the legs of the right triangle and c be the hypotenus

a = x cm

b = 2x + 2 cm

c = 3x - 2 cm

using pythagoreas theorem–

c² = a² + b²

(3x - 2)² = (x)² + (2x + 2)²

9x² - 12x + 4 = x² + 4x² + 8x + 4

9x² - 12x + 4 = 5x² + 8x + 4

9x² - 5x² - 12x - 8x + 4 - 4 = 0

4x² - 22x = 0

2x(2x - 11) = 0

hence

2x = 0 or 2x - 11 = 0

x = 0 or x = 11/2

but, since a = x

x≠0 or the triangle would not have existed

hence, x = 11/2

hence a = 11/2 cm = 5.5 cm

b = 2x + 2 = 2(11/2) + 2 = 11 + 2 = 13 cm

c = 3x - 2 = 3(11/2) - 2 = (33/2) - 2 = (33 - 4)/2 = 29/2

c = 14.5 cm

Hence, the measures of sides if the given right triangle is 5.5 cm, 13 cm and 14.5 cm.

Answer 2

Answer:

(3x-2) 2 = x2 + (2x+2) 2

9x2-12x+4= x2+4x2 +8x +4

4x2-20x = 0

x2-5x=0

x(x-5)=0

x = 0 or 5

sides. x=5, 2x +2=12

hypot=3x-2 = 13

Sides of the triangle = 5, 12,13