Question

The perimeter of a triangle is 93 ft. Side a of the triangle is twice as long as side b. Side c is 3 ft longer than side a. Find the length of each side.

Answer 1

The length of side a is 36 feet and side b is 18 feet and side c is 39 feet

Solution:

Given that perimeter of triangle is 93 feet

The three sides of triangle are a, b, and c

Given that Side a of the triangle is twice as long as side b

side a = 2 times side b

a = 2b

$b = \frac{a}{2}$  ---- eqn 1

Given that Side c is 3 ft longer than side a

side c = 3 + side a

c = 3 + a ------ eqn 2

The perimeter of triangle is given as:

p = a + b + c

Where a, b, c are the length of sides of triangle

Substitute eqn 1 and eqn 2 in above formula

$p = a + \frac{a}{2} + 3 + a$

Given that perimeter = 93

$93 = a + \frac{a}{2} + 3 + a\\\\93 = \frac{2a + a + 6 + 2a}{2}\\\\93 \times 2 = 2a + a + 6 + 2a\\\\186 = 5a + 6\\\\5a = 186 - 6\\\\5a = 180\\\\a = 36$

Thus length of side a = 36 feet

Length of side b :

from eqn 1

$b = \frac{36}{2} = 18$

b = 18 feet

Length of side c:

From eqn 2,

c = 3 + 36 = 39

c = 39 feet

Thus length of side a is 36 feet and side b is 18 feet and side c is 39 feet