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5-65.

Find the missing side lengths of each rectangle, (a) and (c) or square (b) and (d). Homework Help ✎

1. $\qquad \qquad \qquad \ x\ \text{cm}\\ 100\ \text{cm}\ \begin{array} {|c|}\hline\\ \quad \text{A}=500 \ \text{cm}^2 \quad\\ \\ \hline \end{array}$

To find the area of a rectangle, multiply the length
by the width.

$(100\text{ cm})(x\text{ cm})=500\text{ cm}^2$

Solve for $x$.

1. $\qquad \ y\ \text{cm}\\ \begin{array} {|c|}\hline\\ \\ \ \ \text{A}=64 \ \text{cm}^2 \ \ \\ \\ \\ \hline \end{array} \ 8 \ \text{cm}$

Recall the properties of a square. All the side lengths must be equal.

Since one side is already given, you can conclude that the other side is also $8$ cm.

1. $\qquad 5\ \text{cm}\\ r\ \text{cm} \begin{array} {|c|}\hline\\ \quad \\ \\ \hline \end{array} \longleftarrow \text{A}=82 \ \text{cm}^2$

See the help for part (a).

$16.4$ cm

1. $\begin{array} {|c|}\hline\\ \text{A}= \\\quad 25 \ \text{cm}^2 \quad \\ \\ \hline \end{array} \ w \ \text{cm}\\ \quad \quad \ 5 \text{cm}$

See the help for part (b).