Question

Find the area of a triangle whose perimeter is 180 cm and two of sides are 80 cm and 18 cm.also calculate the altitude of the triangle corresponding to the short side.

Answer 1

hello dear

given the perimeter of the triangle = 180cm

therefore semi-perimeter of the triangle = 180/2 = 90cm

let the sides of the triangle be a, b and c.

>> a + b + c = 180cm

>> 80 + 18 + c = 180cm

>> 98 + c = 180cm

>> c = 180 - 98

>> c = 82cm

area of the triangle by Heron's formula = √[s(s-a)(s-b)(s-c)]

= √[90(90-80)(90-18)(90-82)]

= √(90×10×72×8)

= √518400

= 720cm²

ATQ, now we have to find the altitude of the triangle corresponding to the shortest side.

here shortest side is b = 18cm

let it be the base.

therefore altitude × base = area

>> altitude = area/base

>> altitude = 720/18

>> altitude = 40cm

hence, the altitude of the triangle is 40 cm.