Answer:
shorter side = 5 feet, middle side = 15 feet, and longest side = 23 feet
Step-by-step explanation:
Given the perimeter of the triangle = 43 feet
Let the length of the middle side be represented by a. Then;
shortest side = [tex]\frac{1}{3}[/tex] x a
= [tex]\frac{a}{3}[/tex] feet
longest side = (4 x [tex]\frac{a}{3}[/tex]) + 3
= [tex]\frac{4a}{3}[/tex] + 3
Perimeter = a + [tex]\frac{a}{3}[/tex] + ([tex]\frac{4a}{3}[/tex] + 3)
⇒ 43 = a + [tex]\frac{a}{3}[/tex] + [tex]\frac{4a}{3}[/tex] + 3
43 - 3 = a + [tex]\frac{a}{3}[/tex] + [tex]\frac{4a}{3}[/tex]
40 = [tex]\frac{3a+a+4a}{3}[/tex]
= [tex]\frac{8a}{3}[/tex]
40 x 3 = 8a
120 = 8a
a = [tex]\frac{120}{8}[/tex]
= 15
Therefore,
middle side = 15 feet
shorter side = [tex]\frac{a}{3}[/tex] = [tex]\frac{15}{3}[/tex]
= 5 feet
longest side = (4 x [tex]\frac{a}{3}[/tex]) + 3
= (4 x 5) + 3
= 23 feet
