Thread: 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?

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.









This is the shortest side of the smaller triangle

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



Solve the proportion and you have the shorter side of the larger triangle.

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, , we have: .

. .

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?