The area of a square is 81 square centimeters. What is the length of the diagonal?

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The area of a square is 81 square centimeters. What is the length of the diagonal?

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Answer 1 · 2015-11-13T06:31:32

If you note that $81$ $81$ is a perfect square, you can say that for a real square shape:

$\sqrt{81} = 9$ $sqrt(81) = 9$

Furthermore, since you have a square, the diagonal, which forms a hypotenuse, creates a $45^{\circ} - 45^{\circ} - 90^{\circ}$ $45^@-45^@-90^@$ triangle.

So, we would expect the hypotenuse to be $9 \sqrt{2}$ $9sqrt2$ since the general relationship for this special type of triangle is:

$a = n$ $a = n$
$b = n$ $b = n$
$c = n \sqrt{2}$ $c = nsqrt2$

Let's show that $c = 9 \sqrt{2}$ $c = 9sqrt2$ using the Pythagorean Theorem.

$c = \sqrt{a^{2} + b^{2}}$ $c = sqrt(a^2 + b^2)$

$= \sqrt{9^{2} + 9^{2}}$ $= sqrt(9^2 + 9^2)$

$= \sqrt{81 + 81}$ $= sqrt(81 + 81)$

$= \sqrt{2 \cdot 81}$ $= sqrt(2*81)$

$= 9 \sqrt{2} cm$ $= color(blue)(9sqrt2 " cm"$

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The area of a square is 81 square centimeters. What is the length of the diagonal?

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