Question

An isosceles triangle has perimeter 30 cm and the base of the triangle is 6cm. Find the area of the triangle by heron's formula

Answer 1

in an isosceles triangle 2 sides are equal.

let the 2 side those are equal be x

base = 6cm........given

let base be y

perimeter = sum of all sides

60 = x+x+y

60 = 2x+6

60-6 = 2x

58 = 2x

58/2 = x

x = 29cm

${s}^{1} = 6 \\ {s}^{2} = 29 \\ {s}^{3} = 29 \\ \\ semi \: perimeter \: = \frac{60}{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 30 \\ \\ s = 30 \\ area = \sqrt{s \times (s - {s}^{1}) \times (s - {s}^{2} ) \times (s - {s}^{3} } \\ area = \sqrt{s \times (30 - 6) \times (30- 29) \times (30 \: - 29) } \\ area = \sqrt{30 \times 24 \times 1 \times 1} \\ area = \sqrt{720} \\ area = \sqrt{2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5} \\ area = 2 \times 2 \times 3\sqrt{5} \\ area = 12 \sqrt{5} \: \: {cm}^{2}$

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