Question

A triangular sail has a perimeter of 25 m. Side a is 2 m shorter than twice side b, and side c is 3 m longer than side b. Find the length of each side.

Answer 1

Given :

• Perimeter of triangular sail = 25 m
• Side 'a' is 2m shorter than twice of side 'b'
• Side 'c' is 3m longer than side 'b'

To find :

Length of each side

Formula used :

Perimeter of triangle = Sum of all side

Solution :

Let - Side b = x m

Therefore, side a = 2b - 2

side a = (2x - 2)m

Side c = 3m + x m

side c = (3+ x) m

Now perimeter of triangular sail = side a + side b + side c

Perimeter of triangular sail = (2x-2) + (x) + (3+x)

Perimeter of triangular sail = 2x - 2 + x + 3 + x

Perimeter of triangular sail = 4x + 1

Now according to question, Perimeter of triangular sail = 25m

Therefore, 4x + 1 = 25

4x = 25 - 1

4x = 24

x = 24 ÷ 4

x = 6

Therefore ,

1) side b = x = 6m

2) side a = (2x-2) m

side a = 2(6) - 2 m

side a = 12 - 2 m

side a = 10m

3) side c = 3 + x

side c = 3 + 6m

side c = 9 m

ANSWER :

• Side a = 10 m
• Side b = 6 m
• Side c = 9 m