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.

Question

What is the value of x?

Answer 1

To find the value of \( x \) where the area of the rectangle is equal to the area of the triangle, we start by calculating both areas.

Area of the rectangle: \[ \text{Area}{\text{rectangle}} = \text{length} \times \text{width} = (5 + 2x) \times 10 \] \[ \text{Area}{\text{rectangle}} = 10(5 + 2x) = 50 + 20x \quad \text{(in square inches)} \]

Area of the triangle: \[ \text{Area}{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 30 \times (4x - 10) \] \[ \text{Area}{\text{triangle}} = 15(4x - 10) = 60x - 150 \quad \text{(in square inches)} \]

Now, we set the area of the rectangle equal to the area of the triangle: \[ 50 + 20x = 60x - 150 \]

Next, we'll solve for \( x \):

1. Rearranging the equation: \[ 50 + 150 = 60x - 20x \] \[ 200 = 40x \]

2. Divide both sides by 40: \[ x = \frac{200}{40} = 5 \]

Thus, the value of \( x \) is: \[ \boxed{5} \]