Question

The cross-section of a lean-to shelter is in the shape of a triangle. The base of the
triangle is 4 feet more than twice its height. If the area of the triangle is 63 square feet,
determine the length of the base and the height of the triangle in feet.

Answer 1

Answer:

height = 7 ft

base = 18 ft

Step-by-step explanation:

Area of a Triangle

$\sf A=\dfrac{1}{2}bh$

where:

• A = area
• b = base
• h = height

If the base of the triangle is 4 feet more than twice its height, then:

• b = 2h + 4

Substitute the given area and the found expression for b into the formula and solve for h:

$\begin{aligned}\sf A & = \sf \dfrac{1}{2}bh\\\implies \sf 63 & = \sf \dfrac{1}{2}(2h+4)h\\\sf 126 & = \sf (2h+4)h\\\sf 126 & = \sf 2h^2+4h\\\sf 2h^2+4h-126 & = \sf 0\\\sf 2(h^2+2h-63) & = \sf 0\\\sf h^2+2h-63 & = \sf 0\\ \sf h^2+9h-7h-63 & = \sf 0\\ \sf h(h+9)-7(h+9) & \sf = \sf 0\\\sf (h-7)(h+9) & = \sf 0\\\implies \sf h& = \sf 7, -9\end{aligned}$

As length is positive, h = 7 ft.

Substitute the found value of h into the expression for b and solve for b:

$\begin{aligned}\sf b & = \sf 2h+4\\\implies \sf b & = \sf 2(7)+4\\& = \sf 14+4\\& = \sf 18\end{aligned}$

Therefore, b = 14 ft.