Question

The sides of a triangle are in the ratio 4:5:7. If the perimeter of the triangle is 32cm Find the area of the Triangle.​

Answer 1

Answer:

area of triangle is 16√6.

Answer 2

GIVEN :-

• Ratio of triangle are in ratio 4:5:7.
• Perimeter of the triangle is 32cm.

TO FIND :-

• Area of the triangle.

SOLUTION :-

Let the sides of the triangle be 4x , 5x and 7x respectively as ratio is 4:5:7.

Perimeter = Sum of all sides

→ 32 = 4x + 5x + 7x

→ 32 = 16x

→ x = 32/16

→ x = 2

Sides are :-

• 4x = 4(2) = 8cm
• 5x = 5(2) = 10cm
• 7x = 7(2) = 14cm

Hence , sides of the triangle are 8cm , 10cm and 14cm. Perimeter is 32cm.

For area ,

$\\ \boxed{\sf \: area = \sqrt{s(s - a)(s - b)(s - c)} }$

Here ,

• s → Semi-perimeter
• a ,b ,c → Sides of triangle

We have,

• s = 32/2 = 16cm
• a = 8cm
• b = 10cm
• c = 14cm

Putting values we get,

$\\ \sf \: area = \sqrt{16(16 - 8)(16 - 10)(16 - 14)} \\ \\ \sf \: area = \sqrt{16(8)(6)(2)} \\ \\ \sf \: area = \sqrt{1536} \\ \\ \boxed{\sf \: area = 39.2 {cm}^{2} }$

Hence , area of triangle is 39.2cm².