Question

The two perpendicular sides of a right-angled triangle are in the ratio 3:4 and
its perimeter is 96 cm. Find the three sides

Answer 1

Answer:

Since it a right angled triangle, and as the two perpendicular sides are in the ratio of 3:4, the third sides needs to be proportional to 5.

As in a right angled triangle,

Hypotenuse^2 = base^2 + perpendicular^2

Therefore, the sides are in the ratio of

3 : 4 : 5

Sum of the ratios = 3 +4 +5 = 12

Perimeter of triangle = 96 cm

Therefore the sides are = (96*3/12), (96*4/12), (96*5/12) = 24 cm,32, cm and 40 cm.

Answer 2

Given:

Ratio of the sides = 3:4

Perimeter = 96cm

To find:

The three sides

Solution:

Let the two perpendicular sides be 3x and 4x

Therefore applying the Pythagoras theorem,

Hypotenuse = √ [ (3x)² + (4x)² ]

= √ [ 9x² + 16x² ]

= √25x²

= 5x

Now,

Perimeter = sum of three sides

therefore 96 = 3x + 4x + 5x

96 = 12x

x = 8

Substituting the value -

= 3x = 3(8) = 24

= 4x = 4(8) = 32

= 5x = 5(8) = 40

Answer: The three sides are 24cm, 32cm, and 40cm.