The diagonal of a rectangle measures 25cm. The width of the rectangle is 7cm. How do you find the length of the rectangle in cm?

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The diagonal of a rectangle measures 25cm. The width of the rectangle is 7cm. How do you find the length of the rectangle in cm?

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Answer 1 · 2015-10-14T03:10:28

The height (length) is $24 cm$ $"24 cm"$ .

Explanation:

![http://gifsgallery.com/right+triangle+gif?image=212188146]( useruploads.socratic.org )

The diagonal of a right triangle is the hypotenuse and is designated as side $c$ $c$ . The width of a right triangle is side $b$ $b$ , and the height is side $a$ $a$ . You are looking for side $a$ $a$ .

The Pythagorean equation is $c^{2} = a^{2} + b^{2}$ $c^2=a^2+b^2$ .
$c = 25 cm$ $c="25 cm"$
$b = 7 cm$ $b="7 cm"$
$a = ?$ $a=?$

Rearrange the equation to solve for side $a$ $a$ .

$a^{2} = c^{2} - b^{2}$ $a^2=c^2-b^2$

Substitute the known values into the equation.

$a^{2} = {(25 cm)}^{2} - {(7 cm)}^{2} =$ $a^2=(25"cm")^2-(7"cm")^2=$

$a^{2} = 625 {cm}^{2} - 49 {cm}^{2} =$ $a^2=625"cm"^2"-"49"cm"^2=$

$a^{2} = 576 {cm}^{2}$ $a^2=576"cm"^2$

Take the square root of both sides.

$\sqrt{a^{2}} = \sqrt{576 {cm}^{2}}$ $sqrt(a^2)=sqrt(576"cm"^2")$

$a = 24 cm$ $a="24 cm"$

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The diagonal of a rectangle measures 25cm. The width of the rectangle is 7cm. How do you find the length of the rectangle in cm?

1 Answer

Explanation:

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