Question

the area of a triangle is 93 square feet. the base is four times the height. find the height. you do not need to include the unit measurement or unit type. only the numerical answer is necessary. round to the nearest tenth if necessary.

Explanation:

Step1: Set up the formula for the area of a triangle

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). Let the height \(h = x\), then the base \(b = 4x\). Substitute into the formula: \(93=\frac{1}{2}(4x)x\).

Step2: Simplify the equation

Simplify \(\frac{1}{2}(4x)x\) to \(2x^{2}\). So the equation becomes \(2x^{2}=93\).

Step3: Solve for \(x^{2}\)

Divide both sides of the equation \(2x^{2}=93\) by 2: \(x^{2}=\frac{93}{2}=46.5\).

Step4: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{46.5}\approx6.8\).

Answer:

\(6.8\)