Question

solving equations using perimeter & area of rectangles quiz (8.8c*) eddie has a rectangle with a width of 2.4 cm. if the perimeter and area of the rectangle are the same, what is the length of eddies rectangle? 8 cm 4.8 cm 2.4 cm 12 cm

Explanation:

Step1: Recall rectangle formulas

Let the length be $l$ and width $w = 2.4$ cm. Perimeter $P=2(l + w)$ and area $A=l\times w$. Since $P = A$, we have $2(l + 2.4)=l\times2.4$.

Step2: Expand the left - hand side

Expand $2(l + 2.4)$ to get $2l+4.8$. So the equation becomes $2l + 4.8=2.4l$.

Step3: Solve for $l$

Subtract $2l$ from both sides: $4.8=2.4l-2l$, which simplifies to $4.8 = 0.4l$. Then divide both sides by $0.4$: $l=\frac{4.8}{0.4}=12$ cm.

Answer:

12 cm