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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
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Solution
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
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