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A manufacturer makes trusses, or triangular supports, for the roofs of houses. Each truss is the shape of an isosceles triangle in which PQ ≅ PR. The length of the base QR is 4/3 the length of each of the congruent sides. The perimeter of each truss is 70 ft. Find each side length.

What is the length of each side?

Answer 1

The length of each side of the triangle is;

• Equal sides, x = 21.02 = PQ = PR
• QR = 28.03

The trusses made by the manufacturer have the shape of an isoscelles triangle and as such two congruent sides (PQ ≅ PR) are equal and QR is the third side whose length is 4/3 of the congruent sides.

The perimeter of each truss is 70ft.

Let the length of each congruent side be x ft.

Therefore,

• Perimeter = x + x + (4/3)x

• Perimeter, p = 70 = 3.33x

• x = 70/3.33

• x = 21.02

Therefore, Length of QR is; QR = (4/3) x

• QR = (4/3) × 21.02

• QR = 28.03

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