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Question
In the following figures, perimeter of ΔABC = perimeter of ΔPQR. Find the area of ΔABC.
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Solution
Given, perimeter of ΔABC = perimeter of ΔPQR
Perimeter of APQR = 14 + 6 + 10 = 30 cm ...[∵ Perimeter of triangle = Sum of all sides]
Now, perimeter of ΔABC = AB + BC + CA
30 = AB + BC + AC
⇒ 30 = AB + 5 + 13
⇒ 30 = AB + 18
⇒ AB = 30 – 18 = 12 cm
∴ Area of ΔABC = `1/2` × Base × Height
= `1/2 xx 5 xx 12`
= 5 × 6
= 30 cm2
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