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 \(A_{r}=\text{length}\times\text{width}=(5 + 2x)\times10=50+20x\).
Area of triangle \(A_{t}=\frac{1}{2}\times\text{base}\times\text{height}=\frac{1}{2}\times30\times(4x - 10)=15\times(4x - 10)=60x-150\).

Step2: Set areas equal and solve for \(x\)

Since \(A_{r}=A_{t}\), we have \(50 + 20x=60x-150\).
Subtract \(20x\) from both sides: \(50=40x-150\).
Add \(150\) to both sides: \(200 = 40x\).
Divide both sides by \(40\): \(x = 5\).

Answer:

D. 5