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Question
Area of an isosceles triangle is 48 cm2. If the altitudes corresponding to the base of the triangle is 8 cm, find the perimeter of the triangle.
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Solution
Given, area of ΔABC = 48 cm2 and altitude = 8 cm
∵ ΔABC is an isosceles triangle, where AB = AC
∴ Area of ΔABC = `1/2` × BC × AD = 48 ...[∵ Area of triangle = Base × Height]
⇒ 48 = `1/2` × BC × AD
⇒ `1/2` × BC × 8 = 48
⇒ BC = `(48 xx 2)/8`
BC = 12 cm
Now, in an isosceles triangle, BD = DC = 6 cm ...[∵ AD ⊥ BC]
Applying Pythagoras theorem in right-angled ΔADB,
AB2 = BD2 + AD2
⇒ AB2 = 62 + 82 = 36 + 64
⇒ AB2 = 100
⇒ AB = 10 cm
Now, perimeter of triangle = AB + AC + BC
= AB + AB + BC ...[∵ AB = AC]
= 10 + 10 + 12
= 32 cm
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