Question

a rectangle has a length of $(5 + 2x)$ inches and a width of 10 inches. a triangle has a base of 30 inches and a height of $(4x - 10)$ inches. the area in square inches of the rectangle is equal to the area in square inches of the triangle. what is the value of $x$? a 2.5 b 3 c 7.5 d 5

Explanation:

Step1: Write area formulas

Area of rectangle \(A_{r}=\text{length}\times\text{width}=(5 + 2x)\times10\).
Area of triangle \(A_{t}=\frac{1}{2}\times\text{base}\times\text{height}=\frac{1}{2}\times30\times(4x - 10)\).

Step2: Set up equation

Since \(A_{r}=A_{t}\), we have \((5 + 2x)\times10=\frac{1}{2}\times30\times(4x - 10)\).

Step3: Simplify equation

Expand: \(50+20x = 15\times(4x - 10)\).
\(50+20x=60x-150\).

Step4: Solve for \(x\)

Move terms: \(20x-60x=-150 - 50\).
\(-40x=-200\).
\(x = 5\).

Answer:

D. 5