Question

find the value of x so that the two rectangles have the same area. 4 cm x cm 8 cm 7 cm x cm 2 cm

Explanation:

Step1: Calculate area of first rectangle

The first rectangle has length $(x + 8)$ cm and width 4 cm. So its area $A_1=4(x + 8)=4x+32$ (using the formula $A = lw$, where $l$ is length and $w$ is width).

Step2: Calculate area of second rectangle

The second rectangle has length 7 cm and width $(x + 2)$ cm. So its area $A_2=7(x + 2)=7x+14$.

Step3: Set areas equal

Since the two rectangles have the same area, we set $A_1 = A_2$. So $4x+32=7x + 14$.

Step4: Solve for x

Subtract $4x$ from both sides: $32=3x + 14$. Then subtract 14 from both sides: $3x=32 - 14=18$. Divide both sides by 3: $x = 6$.

Answer:

$x = 6$