Question

Area of ΔABD = 30 cm². Find the area of ΔADC, if BD = `5/8` BC.

Answer 1

Given:

• Area of ΔABD = 30 cm²
• BD = `5/8` BC

Since ΔABD and ΔADC share the same height from A to line BC, the areas of these triangles will be proportional to their bases BD and DC respectively.

Let BC = x

Then BD = `5/8`x and DC = BC − BD = x − `5/8`x = `3/8`x

`("Area of"  ΔABD)/("Area of"  ΔADC) = (BD)/(DC) = (5/8 x)/(3/8 x) = 5/3`

Given area of ΔABD = 30 cm², let area of ΔADC = y cm².

Therefore, `30/y = 5/3`

Cross multiply: 5y = 90

Solving for y,

y = `90/5` = 18 cm².

Area of ΔADC = 18 cm².