Question

The perimeter of a triangle is 300 m . If its sides are in the ratio 3:5:7. Find the area of the triangle.

Answer 1

Answer:

A ≈ 1500$\sqrt{3}$ m²

Step-by-step explanation:

sum the parts of the ratio, 3 + 5 + 7 = 15 parts

Divide perimeter by 15 to find the value of one part of the ratio.

300 ÷ 15 = 20 m ← value of 1 part of the ratio , then

3 parts = 3 × 20 = 60 m

5 parts = 5 × 20 = 100 m

7 parts = 7 × 20 = 140 m

The 3 sides of the triangle are 60 m, 100 m , 140 m

To calculate the area (A) having all 3 sides use Hero's formula

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

where s is the semiperimeter and a, b , c the sides of the triangle

s = 300 m ÷ 2 = 150 m

let a = 60, b = 100 and c = 140 , then

A = $\sqrt{150(150-60)(150-100)(150-140)}$

   = $\sqrt{150(90)(50)(10)}$

   = $\sqrt{6750000}$

   = $\sqrt{10000}$ × $\sqrt{675}$

   = 100 × $\sqrt{25(27)}$

    = 100 × 5$\sqrt{27}$    

    = 500 × $\sqrt{9(3)}$

   = 500 × 3$\sqrt{3}$

   = 1500$\sqrt{3}$ m²

Answer 2

Answer:

If the perimeter = 300m

let the ratio be in x

a/q.

3x + 5x + 7x. = 300m

15x = 300

x = 300/15

x = 20

hence angles are

60 , 100 and 140

hope it helps