Question

find the value of x so that the two rectangles have the same area. 6 cm x cm 8 cm 8 cm x cm 5 cm x =

Explanation:

Step1: Calculate area of first rectangle

The area of the first rectangle with length $(x + 8)$ cm and width $6$ cm is $A_1=6(x + 8)=6x+48$.

Step2: Calculate area of second rectangle

The area of the second rectangle with length $8$ cm and width $(x + 5)$ cm is $A_2=8(x + 5)=8x+40$.

Step3: Set areas equal

Since the two rectangles have the same area, we set $A_1 = A_2$. So, $6x+48=8x + 40$.

Step4: Solve for x

Subtract $6x$ from both sides: $48=2x + 40$. Then subtract $40$ from both sides: $8 = 2x$. Divide both sides by $2$: $x = 4$.

Answer:

$4$