The lengths of the two sides of a right triangle containing the right

1.	The lengths of the two sides of a right triangle containing the right angle differ by 2 cm. If the area of the triangle is 24 cm2, find the perimeter of the triangle.
Answer» Let x cm be the one of the sides, then (x – 2) cm be another side. Area of triangle = 24 cm² (given) We know, Area of triangle = 1/2(Base x height) 24 = 1/2(x (x – 2)) 48 = x² – 2x or x² – 2x – 48 = 0 Solving above equation, we have (x + 6)(x – 8) = 0 x = -6 or x = 8 Since length measure cannot be negative, so neglect x = -6 One side = 8 cm Another Side = x – 2 = 8 – 2 = 6 cm Apply Pythagoras theorem: Hypotenuse² = Base² + Perpendicular² Hypotenuse² = √(8² + 6²) Hypotenuse = √100 = 10 Therefore, perimeter of triangle = Sum of all the sides = (6 + 8 + 10) cm = 24 cm

The lengths of the two sides of a right triangle containing the right angle differ by 2 cm. If the area of the triangle is 24 cm2, find the perimeter of the triangle.

Answer»

Let x cm be the one of the sides, then (x – 2) cm be another side.

Area of triangle = 24 cm² (given)

We know, Area of triangle = 1/2(Base x height)

24 = 1/2(x (x – 2))

48 = x² – 2x

or x² – 2x – 48 = 0

Solving above equation, we have

(x + 6)(x – 8) = 0

x = -6 or x = 8

Since length measure cannot be negative, so neglect x = -6

One side = 8 cm

Another Side = x – 2 = 8 – 2 = 6 cm

Apply Pythagoras theorem:

Hypotenuse² = Base² + Perpendicular²

Hypotenuse² = √(8² + 6²)

Hypotenuse = √100 = 10

Therefore, perimeter of triangle = Sum of all the sides = (6 + 8 + 10) cm = 24 cm