Question

a triangle whose side are in the ratio of 2:7:5 and it's perimeter is 280m. find it's area​

Answer 1

Step-by-step explanation:

let x be the proportion

=> 2x + 7x + 5x = 140

=> 14x = 140

=> x = 10 ie,

a = 2 (10) = 20cm b = 7 (10) = 70cm c = 5 (10) = 50cm

By Herons formula, Area of a triangle,

A = Vs (s - a) (s - b) (s -c)

where s = half of perimeter

here s = 140/2 = 70

so Area, A = V70 (70 - 20) (70 - 70) (70 - 50) = 0

=> The triangle is actually a line.

(3 vertices lying on the same line)

Answer 2

THE SIDES OF THE TRIANGLE ARE 2x, 7x, 5x

Given,

Perimeter of triangle = 2x + 7x + 5x = 280

$\implies \tt{2x + 7x + 5x = 280} \\ \\ \implies \tt 14x = 280 \\ \\ \implies \tt \frac{14x}{14} = \frac{280}{14} \\ \\ \implies \tt \: x = 20$

Thus,

• 1st side = 40 m
• 2nd side = 140 m
• 3rd side = 100 m