Special Right Triangles

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PrinceGetapeTyro

Asked: April 8, 20212021-04-08T04:18:09+00:00 2021-04-08T04:18:09+00:00In: Geometry, High School/Senior Secondary School

If the are of square is 121cm², find the length of the sides and the diagonal of the square.

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acedstud · Answer 1 · 2021-04-08T05:27:34+00:00

The area of a square of sides of length $l$ is given by $l^2$ .

Thus, $l^2=121\Rightarrow l=\sqrt{121}=11$ .

Thus, the length of the sides of the square is 11 cm.

Now, the sides of a square make a right triangle with the diagonal of the square where the sides are the legs and the diagonal is the hypotenuse.

Thus, we are looking for the hypotenuse of a right triangle with the length of the 2 legs equal to 11 cm.

Let the length of the hypotenuse be $r$ , then using the Pythagoras theorem, $r^2=11^2+11^2=121+121=242$

Taking the square root of both sides gives $\sqrt{r^2}=\sqrt{242}=\sqrt{121\times2}=\sqrt{121}\times\sqrt{2}=11\sqrt{2}$ .

Thus, $r=11\sqrt{2}\approx15.56$ cm.

Therefore, the length of the sides of the square is 11 cm and the length of the diagonal is $11\sqrt{2}$ cm.

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