Question

if the base of an isosceles triangle is 12cm and its perimeter is 35 cm find the area of triangle​

Answer 1

Perimeter of an isosceles triangle = 35 cm

Base side = 12 cm

perimeter of a triangle = sum of all sides

An isosceles triangle has two equal sides so let the two equal sides be x and x = 2 x and the third side is 12 cm as given in the question...

35 = 2 x + 12

35  - 12 = 2 x

23 = 2  x

x = 23/ 2

x = 11.5 cm

so the two equal sides are 11.5 cm each....

$Area \ of \ triangle = \sqrt{s(s-a)(s-b)(s-c)} \\\\s = semi perimeter = \frac{perimeter }{2} \\\\s = \frac{35}{2} = 17.5\\\\here \ a = 12 \ , b = 11.5 \ , c = 11.5 \\\\area = \sqrt{17.5(17.5-12)(17.5-11.5)(17.5-11.5)} \\\\area = \sqrt{17.5 * 5.5 * 6 * 6} \\\\area =6 \sqrt{96.25}$

hope it helps !!