Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The height of a triangular truss is $5 \mathrm { ft }$ less than the base. The amount of drywall needed to cover the triangular area is $84 \mathrm { ft } ^ { 2 }$. Find the base and height of the triangle to the nearest tenth of a foot.
A) base $= 15.9 \mathrm { ft }$; height $= 10.9 \mathrm { ft }$
B) base $= 12 \mathrm { ft }$; height $= 7 \mathrm { ft }$
C) base $= 21 \mathrm { ft }$; height $= 16 \mathrm { ft }$
D) base $= 15.7 \mathrm { ft }$; height $= 10.7 \mathrm { ft }$

Question

Quizplus · Accepted Answer

The area of a triangle is given by $ \frac{1}{2} \times \text{base} \times \text{height} $. Given that the height is 5 ft less than the base, we can set up the equation $ \frac{1}{2} \times b \times (b - 5) = 84 $. Solving this quadratic equation for $ b $ gives us the base, and subtracting 5 from the base gives us the height. The closest values that satisfy this condition are base = 15.7 ft and height = 10.7 ft.

Write the Word or Phrase That Best Completes Each Statement 5ft5 \mathrm { ft }5ft

Write the Word or Phrase That Best Completes Each Statement $5 \mathrm { ft }$