A right triangle has a side length of 21 inches and a hypotenuse of 29 inches. A second triangle is similar to the first and has a hypotenuse of 87 inches. what is the length of the shortest side of the second triangle?

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- Nov 2nd 2008, 10:15 AMxsrieltriangle
A right triangle has a side length of 21 inches and a hypotenuse of 29 inches. A second triangle is similar to the first and has a hypotenuse of 87 inches. what is the length of the shortest side of the second triangle?

- Nov 2nd 2008, 02:01 PMmasters
Set up a proportion to match up corresponding sides. But first we need to find the third side of your first triangle.

$\displaystyle c^2=a^2+b^2$

$\displaystyle 29^2=21^2+b^2$

$\displaystyle b^2=29^2-21^2$

$\displaystyle b=\sqrt{29^2-21^2}$

$\displaystyle x=20$ This is the shortest side of the smaller triangle

Now set up the proportion: Smaller triangle to larger triangle:

$\displaystyle \frac{29}{87}=\frac{20}{y}$

Solve the proportion and you have the shorter side of the larger triangle. - Nov 2nd 2008, 02:16 PMSoroban
Hello, xsriel!

This doesn't require any fancy math . . .

Quote:

A right triangle has a side of 21 inches and a hypotenuse of 29 inches.

A second triangle is similar to the first and has a hypotenuse of 87 inches.

What is the length of the shortest side of the second triangle?

Using Pythagorus, $\displaystyle a^2+b^2 \:=\:c^2$, we have: .$\displaystyle a^2 + 21^2 \:=\:29^2 $

. . $\displaystyle a^2 + 441 \:=\:841\quad\Rightarrow\quad a^2 \:=\:400\quad\Rightarrow\quad a = 20$

The first right triangle has side of 20, 21, 29.

It looks like this:Code:`*`

29 * *

* * 20

* *

* * * * *

21

The second right triangle is similar to the first

. . and has a hypotenuse of 87.

It looks like this:Code:`*`

* *

* *

87 * *

* *

* *

* *

* *

* * * * * * * * *

. . So the*entire triangle*is three times as large.

Got it?