Question

find the value of x so that the two rectangles have the same area.

Explanation:

Step1: Calculate area of first rectangle

The area of a rectangle is length times width. For the first rectangle, the length is $(x + 8)$ cm and the width is 4 cm. So the area $A_1=4(x + 8)$.

Step2: Calculate area of second rectangle

For the second rectangle, the length is 7 cm and the width is $(x + 2)$ cm. So the area $A_2=7(x + 2)$.

Step3: Set areas equal and solve for x

Since $A_1 = A_2$, we have the equation $4(x + 8)=7(x + 2)$.
Expand both sides:
$4x+32 = 7x+14$.
Subtract $4x$ from both sides:
$32=7x - 4x+14$,
$32 = 3x+14$.
Subtract 14 from both sides:
$3x=32 - 14$,
$3x = 18$.
Divide both sides by 3:
$x=\frac{18}{3}=6$.

Answer:

$6$