The difference between the sides at right angle in a right-angled tria

1.	The difference between the sides at right angle in a right-angled triangle is 7 cm. The area of the triangle is 60 cm2. Find its perimeter.
Answer» Let x cm be the one of the sides, then (x – 7) cm be another side. Area of triangle = 60 cm² (given) We know, Area of triangle = 1/2(Base x height) 60 = 1/2(x (x – 7)) 120 = x² – 7x or x² – 7x – 120 = 0 Solving above equation, we have (x – 15)(x + 8) = 0 x = 15 or x = -8 Since length measure cannot be negative, so neglect x = -8 One side = 15 cm Another Side = x – 7 = 15 – 7 = 8 cm Apply Pythagoras theorem: Hypotenuse² = Base² + Perpendicular² Hypotenuse² = √(15² + 8²) Hypotenuse = √289 = 17 Therefore, perimeter of triangle = Sum of all the sides = (15 + 8 + 17) cm = 40 cm

The difference between the sides at right angle in a right-angled triangle is 7 cm. The area of the triangle is 60 cm2. Find its perimeter.

Answer»

Let x cm be the one of the sides, then (x – 7) cm be another side.

Area of triangle = 60 cm² (given)

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

60 = 1/2(x (x – 7))

120 = x² – 7x

or x² – 7x – 120 = 0

Solving above equation, we have

(x – 15)(x + 8) = 0

x = 15 or x = -8

Since length measure cannot be negative, so neglect x = -8

One side = 15 cm

Another Side = x – 7 = 15 – 7 = 8 cm

Apply Pythagoras theorem:

Hypotenuse² = Base² + Perpendicular²

Hypotenuse² = √(15² + 8²)

Hypotenuse = √289 = 17

Therefore, perimeter of triangle = Sum of all the sides = (15 + 8 + 17) cm = 40 cm