Question

FIND THE AREA OF AN ISOSCELES TRIANGLE WHERE BASE IS 18CM AND PERIMETER IS 48CM​

Answer 1

let the perimeter of Isosceles Triangle is p

a, a, b are three sides of given triangle

$p = 2a + b \: \: \: \: - - - (1) \\ b = 18cm \\ p = 48cm \\ using \: equation \: (1) \\ 48 = 2a + 18 \\ a = 15 \\ we \: know \: that \: area \: = \frac{1}{2} base \times height \: \: - - -(2)\\ base = 18cm \\ height \: of \: isosceles \: triangle = \sqrt{ {a}^{2} - \frac{ {b}^{2} }{4} } \\ h = \sqrt{ {15}^{2} - \frac{ {18}^{2} }{4} } \\ h = \sqrt{144} \\ h = 12cm \\ using \: equation \: (2) \\ area = \frac{1}{2} \times 18 \times 12 \\ area = 108 \: {cm}^{2}$

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