Question

The perimeter of a triangle is 288 m and the ratio
of the sides is 3: 4:5. Find the area of the triangle.
​

Answer 1

Question:

The perimeter of a triangle is 288 m and the ratio  of the sides is 3: 4:5. Find the area of the triangle.

Given:

• The perimeter of a triangle is 288 m

• Ratio of sides = 3:4:5

To find:

• Area of the  triangle

Formula Used:

• Perimeter = 3s

• Area = $\sqrt{s(s-a)(s-b)(s-c)}$

Solution:

Let the sides be

side 1 = 3x

side 1 = 4x

side 1 = 5x

Perimeter = 3s

$288 = 3x + 4x + 5x\\\\288 = 12x \\\\x= 288/12\\\\x = 24$

3x = 3 x 24 = 72

4x = 4 x 24 = 96

5x = 5 x 24 = 120

• a = 72 m

• b = 96 m

• c = 120 m

Through herons formula we can find the area when 3 sides are given

$\sqrt{s(s-a)(s-b)(s-c)}$

where ,

a = 72

b = 96

c = 120

$s =\frac{a+b+c}{2}$

s=$\frac{288}{2}$

$s=144cm$

$\sqrt{144(144-72)(144-96)(144-120)}$

$\sqrt{144(72)(48)(24)}$

$\sqrt{11943936\:\: m}$

$= 3456 \:m^2$

Area = 3456 m²

Answer:

Area of the triangle whose perimeter is 288 cm is 3456 m²

Answer 2

Refer to above answer