Question

The length of one side of a triangle is 2 feet less than three times the length of its second side. The length of the third side is 3/4 of the sum of the lengths of the first two sides. Find the lengths of all three sides if the perimeter of the triangle is 17.5 feet.

Answer 1

• 7 feet, 3 feet, 7.5 feet

Explanation:

Let the sides be a, b and c.

Given

The length of one side of a triangle is 2 feet less than three times the length of its second side

• a = 3b - 2

The length of the third side is 3/4 of the sum of the lengths of the first two sides:

• c = (3/4)(a + b)

The perimeter of the triangle is 17.5 feet:

• a + b + c = 17.5

Solution

Substitute a with b in the second equation:

• c = (3/4)(3b - 2 + b) = (3/4)(4b - 2) = (3/4)(4b) - (3/4)(2) = 3b - 1.5

Now substitute a and c with b in the third equation and solve for b:

• a + b + c = 17.5

• 3b - 2 + b + 3b - 1.5 = 17.5
• 7b - 3.5 = 17.5
• 7b = 17.5 + 3.5
• 7b = 21
• b = 3

Find the value of a:

• a = 3b - 2 = 3*3 - 2 = 9 - 2 = 7

Find the value of c:

• c = 3b - 1.5 = 3*3 - 1.5 = 9 - 1.5 = 7.5

The sides of the triangle are:

• a = 7 feet, b = 3 feet, c = 7.5 feet