Question

the dimensions of two rectangles are below. if both rectangles have the same area, what is the value of x? a 0.25 b -1 c 63 d 2.5

Explanation:

Step1: Write area formulas

The area of the first rectangle $A_1 = 7(4x - 1)$. The area of the second rectangle $A_2=9(2x + 2)$. Since $A_1 = A_2$, we have $7(4x - 1)=9(2x + 2)$.

Step2: Expand both sides

Expand the left - hand side: $7\times4x-7\times1 = 28x-7$. Expand the right - hand side: $9\times2x+9\times2=18x + 18$. So the equation becomes $28x-7 = 18x + 18$.

Step3: Move like terms

Subtract $18x$ from both sides: $28x-18x-7=18x-18x + 18$, which simplifies to $10x-7 = 18$. Then add 7 to both sides: $10x-7 + 7=18 + 7$, getting $10x=25$.

Step4: Solve for x

Divide both sides by 10: $x=\frac{25}{10}=2.5$.

Answer:

D. 2.5