Question

There are four right triangles, the ratio of perpendicular sides being 3 : 4 m each. One more fact about each is given below. Find the lengths of the sides of each triangle.

i. The difference in the lengths of the perpendicular sides is 24 metres.

ii. The hypotenuse is 24 metres.

iii. The perimeter is 24 metres.

iv. The area is 24 square metres.

Answer 1

i. Let the perpendicular sides be 3x and 4x

Hypotenuse = \(\sqrt{(3x)^2+(4x)^2}\) = \(\sqrt{9x^2+16x^2}\) = 5x

The difference between the perpendicular sides be,

4x – 3x = x

x = 24

Sides are, 3x = 3 × 24 = 72 m

4x = 4 × 24 = 96 m

5x = 5 × 24 = 120 m

ii. Hypotenuse = 5x = 24

x = \(\frac{24}{5}\) = 4.8

Perpendicular sides 3x = 3 × 4.8 = 14.4 m

4x = 4 × 4.8 = 19.2 m

iii. Perimeter = 3x + 4x + 5x = 12x

12x = 24

x = 2

Sides are, 3x = 3 × 2 = 6m

4x = 4 × 2 = 8 m

5x = 5 × 2 = 10 m

iv. Area = 1/2 × 3x × 4x = 6x²

6x² = 24

x² = 4; x = 2

Sides are, 3x = 3 × 2 = 6m

4x = 4 × 2 = 8m

5x = 5 × 2 = 10 m