How do you find the diagonal of a rectangle whose sides are 20 and 48?

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How do you find the diagonal of a rectangle whose sides are 20 and 48?

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Answer 1 · 2018-04-21T16:46:33

See a solution process below:

Explanation:

The corners of a rectangle are right angles. Therefore, we can find the diagonal of a rectangle using the Pythagorean Theorem where the sides of the rectangle are the sides of the right triangle and the diagonal is the hypotenuse.

The Pythagorean Theorem states:

$a^{2} + b^{2} = c^{2}$ $a^2 + b^2 = c^2$ where $a$ $a$ and $b$ $b$ are the sides of the right triangle and $c$ $c$ is the hypotenuse of the right triangle.

Substituting for $a$ $a$ and $b$ $b$ and solving for $c$ $c$ gives:

$20^{2} + 48^{2} = c^{2}$ $20^2 + 48^2 = c^2$

$400 + 2304 = c^{2}$ $400 + 2304 = c^2$

$2704 = c^{2}$ $2704 = c^2$

$\sqrt{2704} = \sqrt{c^{2}}$ $sqrt(2704) = sqrt(c^2)$

$52 = c$ $52 = c$

$c = 52$ $c = 52$

The diagonal of the rectangle would be 52 units.

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How do you find the diagonal of a rectangle whose sides are 20 and 48?

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