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Question
Each of the equal sides of an isosceles triangle is 4 cm greater than its height. If the base of the triangle is 24 cm; calculate the perimeter and the area of the triangle.
Solution
Let the congruent side of the isosceles triangle be a and the height be h.
Given,
a = h + 4
Since the height of the triangle, divides it into two right angled triangles,
`a^2 = h^2 + (b/2)^2 ⇒ (h + 4)^2 = h^2 + 12^2`
`h^2 + 16 + 8h = h^2 + 144`
8h = 128
h = 16 cm
a = 20 cm
Perimeter of the triangle = Sum of all sides = a + a + b = 20 + 20 + 24 = 64cm
Area of triangle = `1/2` × base × height
= `1/2` × 24 × 16 = 192 sq cm
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