Question

The perimeter of a triangle is 72 cm and its sides are in the ratio

of 5:6:7 find the area of the triangle (please send how u got it in a picture thank u)

Answer 1

235.15 sq.cm

Explanation:

Perimeter:

Perimeter of a triangle is sum of all three sides.

Ratio of sides = 5 : 6 : 7

Sides are 5x , 6x , 7x

Perimeter = 72 cm

5x + 6x + 7x = 72

Combine like terms.

18x = 72

Divide both sides by 18,

x = 72÷ 18

x = 4

5x = 5*4 = 20 cm

6x = 6*4 = 24 cm

7x = 7*4 = 28 cm

Sides: 20cm , 24 cm , 28 cm

So, it is a scalene triangle.

To find the area of scalene triangle use Heron's formula.

a = 20 cm ; b = 24 cm and c = 28 cm

`\sf s = (a + b+ c)/(2) \ where \ s \ is \ the \ semi \ perimeter.`

`\sf =(72)/(2)\\\\\\ = 36 \ cm`

s - a = 36 - 20 = 16 cm

s -b = 36 - 24 = 12 cm

s - c = 36 - 28 = 8 cm

`\sf \boxed{Area = √(s(s-a)(s-b)(s-c))}`

`\sf =√(36*16*12*8)\\\\ = 6*4*4√(6)\\\\= 96 *2.45\\\\=235.15 \ cm^2`