Question

The height of a triangular truss is 6 less than the base. The amount of drywall needed to cover the triangular area is 86ft squared . Find the base and height of the triangle. Round your answer to the nearest tenth of a foot.
The base is approximately...

Answer 1

Answer:

The base of the truss rounded to nearest tenth is 16.5 foot

Explanation:

Assume the base of the triangular truss be x

Then, according to the question, height of truss is 6 less than the base

Therefore, height = x – 6

Given the area is 86 ft squared

Area of a Triangle = ½ × base × height

Substituting the values,

86 = ½ × x × (x – 6)

86 × 2 = x2 – 6x

172 = x2 – 6x

x2 – 6x – 172 = 0

Solving for x;

x = $\frac{-(-6) \pm \sqrt{(-6)^{2}-4(1)(-172)}}{2(1)}$

= $\frac{6 \pm \sqrt{36+688}}{2}=\frac{6 \pm \sqrt{724}}{2}$

=$\frac{6 \pm 26.9072}{2}$

= $\frac{32.9072}{2}$

= 16.4536 = 16.5 foot (rounded to nearest tenth)

Hence, the base of the truss rounded to nearest tenth is 16.5 foot