The hypotenuse of a right triangle is 25 cm. The difference between the lengths of the other two sides of the triangle is 5 cm. Find the lengths of these sides.
Hypotenuse2 = perpendicular2 + base2
Given, hypotenuse of a right triangle is 25 cm. The difference between the lengths of the other two sides of the triangle is 5 cm
Let the base be ‘b’.
⇒ Perpendicular = b – 5
⇒ 252 = b2 + (b – 5)2
⇒ 625 = b2 + b2 + 25 – 10b
⇒ b2 – 5b – 300 = 0
⇒ b2 – 20b + 15b – 300 = 0
⇒ b(b – 20) + 15(b – 20) = 0
⇒ b = 20
Perpendicular = 20 – 5 = 15
Sides are 15 and 20