Question

solving equations using perimeter & area of rectangles quiz (8.8c*) the perimeter and area of the rectangle below is the same. if the width is 10 in, what is the length of the rectangle? the perimeter and area of the rectangle below is the same. if the width is 10 in, what is the length of the rectangle? 10 in 25 in 5 in 10 in 2.5 in

Explanation:

Step1: Write perimeter and area formulas

The perimeter formula of a rectangle is $P = 2(l + w)$, and the area formula is $A=l\times w$. Given $w = 10$ in, and $P = A$. So $2(l + 10)=10l$.

Step2: Expand the left - hand side

Expand $2(l + 10)$ to get $2l+20$. So the equation becomes $2l + 20=10l$.

Step3: Solve for $l$

Subtract $2l$ from both sides: $20 = 10l-2l$, which simplifies to $20 = 8l$. Then divide both sides by 8: $l=\frac{20}{8}=2.5$ in.

Answer:

2.5 in