Question

the sides of a right angle triangle containing the right angle are 4x and 2 X - 1 cm if the area of the triangle is 30 cm square calculate the length of its sides

Answer 1

Given the sides are 4x and (2x - 1)

Solve x:

Area = 1/2 x Length x Breath

30 = 1/2 (4x) (2x - 1)

60 = 4x(2x - 1)

60 = 8x² - 4x

8x² - 4x - 60 = 0

2x² - x - 15 = 0

(x - 3) (2x + 5) = 0

x = 3 or x = -5/3 (rejected, since length cannot be negative)

Find the length of the two sides:

one side = 4x = 4(3) = 12 cm

the other side = 2x - 1 = 2(3) - 1 = 5 cm

Find the third side:

a² + b² = c²

12² + 5² = c²

c² = 144 + 25

c² = 169

c = √169

c = 13 cm

Answer: The length of the sides are 13cm, 12 cm and 5 cm