Question

Ratio of areas of ∆MNO, ∆MOP and ∆MPQ in the following figure is ______.

Options

• 2 : 1 : 3

• 1 : 3 : 2

• 2 : 3 : 1

• 1 : 2 : 3

Answer 1

Ratio of areas of ∆MNO, ∆MOP and ∆MPQ in the following figure is 2 : 1 : 3.

Explanation:

We know that, area of triangle = `1/2` × base × height

So, area of triangle MNO = `1/2` × NO × MO

= `1/2` × 5 × 4

= `1/2` × 20

= 10 cm²

Area of triangle MOP = `1/2` × MO × OP

= `1/2` × 5 × 2

= `1/2` × 10

= 5 cm²

Area of triangle MPQ = `1/2` × MO × PQ  ...[MP = MO]

= `1/2` × 5 × 6

= `1/2` × 30

= 15 cm²

So, the ratio of area = 10 : 5 : 15  ...[Divide each by 5]

Then we get, 2 : 1 : 3