Question

The sides of a triangular plot are in the ratio of 3 : 5 : 7 and its perimeter is 300 m. Find its area. (Use 3 = 1.73)

Answer 1

Answer:

2598 units²

Step-by-step explanation:

Sum the parts of the parts of the ratio 3 + 5 + 7 = 15 parts

Divide the perimeter by 15

300 ÷ 15 = 20 ← value if 1 part, thus sides of triangle are

3 × 20 = 60

5 × 20 = 100

7 × 20 = 140

Using Hero's formula to calculate the area

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

where s is the semi perimeter and a, b , c are the sides of the triangle

s = 300 ÷ 2 = 150

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

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

   = $\sqrt{150(90)(50)(10)}$

   = $\sqrt{6750000}$ ≈ 2598 units²