# triangle

• Nov 2nd 2008, 10:15 AM
xsriel
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?
• Nov 2nd 2008, 02:01 PM
masters
Quote:

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.

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

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

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

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

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

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

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

Solve the proportion and you have the shorter side of the larger triangle.
• Nov 2nd 2008, 02:16 PM
Soroban
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, $a^2+b^2 \:=\:c^2$, we have: . $a^2 + 21^2 \:=\:29^2$

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

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?