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 = [tex]\frac{-(-6) \pm \sqrt{(-6)^{2}-4(1)(-172)}}{2(1)}[/tex]
= [tex]\frac{6 \pm \sqrt{36+688}}{2}=\frac{6 \pm \sqrt{724}}{2}[/tex]
=[tex]\frac{6 \pm 26.9072}{2}[/tex]
= [tex]\frac{32.9072}{2}[/tex]
= 16.4536 = 16.5 foot (rounded to nearest tenth)
Hence, the base of the truss rounded to nearest tenth is 16.5 foot
