# Thread: triangle

1. ## triangle

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?

2. Originally Posted by xsriel
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?
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.

3. Hello, xsriel!

This doesn't require any fancy math . . .

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

Got it?