Question

find the value of x so that the two rectangles have the same area.
7 cm
x cm
7 cm
8 cm
x cm
5 cm
x = \square

Explanation:

Step1: Calculate area of first rectangle

The length of the first rectangle is \(x + 7\) cm and the width is \(7\) cm. So its area \(A_1=7\times(x + 7)\) \(= 7x+49\) \( \text{cm}^2\).

Step2: Calculate area of second rectangle

The length of the second rectangle is \(x + 5\) cm and the width is \(8\) cm. So its area \(A_2 = 8\times(x + 5)\) \(=8x + 40\) \( \text{cm}^2\).

Step3: Set areas equal and solve for x

Since \(A_1=A_2\), we have the equation:
\(7x + 49=8x + 40\)
Subtract \(7x\) from both sides:
\(49=x + 40\)
Subtract \(40\) from both sides:
\(x=49 - 40=9\)

Answer:

\(9\)