Question

The side (in cm) of a triangle containing the right angle are 5x and 3x – 1. If the area of the triangle is 60 cm². Find the sides of the triangle.

Answer 1

Area of the right triangle ABC
= `(5x (3x - 1))/(2)`

∴ `(5x (3x - 1))/(2)` = 60
⇒ 15x² - 5x = 120
⇒ 3x² - x = 24
⇒ 3x² - x - 24 = 0
⇒ 3x² - 9x + 8x - 24 = 0
⇒ 3x(x - 3) + 8(x - 3) = 0
⇒ (x - 3) (3x + 8) = 0
⇒ x - 3 = 0 or 3x + 8 = 0
⇒ x = 3 or x = `(-8)/(3)`
But x = `(-8)/(3)` is not possible as isde cannot be - ve.
Then x = 3.
Hence, sides are AB = 3x - 1 = 8 cm
BC = 5x = 15 cm
Also from AC
= `sqrt(("AB")^2 + ("BC")^2)`
= `sqrt(64 + 225)`
= `sqrt(289)`
= 17 cm.