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About how long, in inches, is the diagonal of a rectangle with side lengths of $7$ and $13$ inches? $\newline$ F. $10$ $\newline$ G. $15$ $\newline$ H. $20$ $\newline$ J. $120$ $\newline$ K. $218$

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Write equations of parabolas in vertex form using properties

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Q. About how long, in inches, is the diagonal of a rectangle with side lengths of

7

and

13

inches?

\newline

F.

10

\newline

G.

15

\newline

H.

20

\newline

J.

120

\newline

K.

218

Use Pythagorean Theorem: To find the length of the diagonal of a rectangle, we use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse $c$ is equal to the sum of the squares of the lengths of the other two sides $a$ and $b$ . The formula is $c^2 = a^2 + b^2$ . For this rectangle, the sides are $7$ inches and $13$ inches. Calculation: $c^2 = 7^2 + 13^2 = 49 + 169 = 218$
Calculate Diagonal Length: Now we need to find the square root of $218$ to get the length of the diagonal. $\newline$ Calculation: $c = \sqrt{218}$ $\newline$ Using a calculator, we find that $\sqrt{218}$ is approximately $14.76$ inches.
Round to Nearest Whole Number: We need to round the result to the nearest whole number to match the answer choices given. $\newline$ Calculation: $14.76$ rounded to the nearest whole number is $15$ .

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