Question

The base and height of a triangle are in the ratio 7 : 5. If the area of the triangle is 280 cm², find its base and height.

Answer 1

Given:

• The base and height of a triangle are in the ratio 7 : 5.
• The area of the triangle is 280 cm².

Stepwise calculation:

1. Let the base = 7x and the height = 5x.   ...(Since their ratio is 7 : 5)

2. The area of a triangle is given by Area = `1/2` × base × height

3. Substitute base and height with 7x and 5x respectively:

`280 = 1/2 xx 7x xx 5x` 

`280 = 1/2 xx 35x^2` 

`280 = (35x^2)/(2)`

4. Multiply both sides by 2: 560 = 35x²

5. Divide both sides by 35: `x^2 = 560/35 = 16`

6. Take the square root: `x = sqrt(16) = 4`

7. Find base and height:

Base = 7x

= 7 × 4

= 28 cm

Height = 5x

= 5 × 4

= 20 cm

The base of the triangle is 28 cm and the height is 20 cm.