Question

the base (unequal side)of an isosceles triangle is 4 cm and its perimeter is 20 cm find its area

Answer 1

Let the sides of the triangle be a, a and b.
b = 4cm

perimeter = 20cm
⇒ a + a + b = 20cm
⇒ 2a + 4 = 20
⇒ 2a = 20 - 4 = 16cm
⇒ a = 16/2 = 8cm

s = perimeter/2 = 20/2 = 10cm

$Area = \sqrt{s(s-a)(s-b)(s-c)}\\ \\ A = \sqrt{10(10-8)(10-8)(10-4)}\\ \\ A = \sqrt{10 \times 2 \times 2 \times 6}= \sqrt{2 \times 5 \times 2 \times 2 \times 2 \times 3}\\ \\ A = 4 \sqrt{15}\ \ cm^2$

Area is 4√15 cm².

Answer 2

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