Question

the equal sides of the isoscales triangle are 12cm , and the perimeter is 30 . the area of this triangle is.
9√15 cm2, 6√15cm2, 3√15cm , √15 . ​

Answer 1

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Perimeter of isosceles triangle = 30cm

Length of equal sides = 12cm

Let third side of triangle = xcm

According to problem,

x + 12 + 12 = 30

x + 24 = 30

x = 30 − 24

x = 6

∴ Third side of triangle = 6cm

Using Heron's formula

Area of triangle = √ s(s−a)(s−b)(s−c) sq. units

where s = a + b + c / 2

s = 30/2 = 15

Area of triangle=

√ 15(15−12)(15−12)(15−6) cm²

= √15×3×3×9 cm²

= 3×3× √15 cm²

= 9√15 cm²

∴ Area of triangle = 9√15 cm²