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
[tex]b = \frac{a}{2}[/tex] ---- 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
[tex]p = a + \frac{a}{2} + 3 + a[/tex]
Given that perimeter = 93
[tex]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[/tex]
Thus length of side a = 36 feet
Length of side b :
from eqn 1
[tex]b = \frac{36}{2} = 18[/tex]
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
