SOLUTION: I am having trouble figuring this question. A rectangular garden has the dimensions 30 feet wide by 16 feet high A pathway cuts diagonally through the garden. What is the lengt

Question 73694: I am having trouble figuring this question. A rectangular garden has the dimensions 30 feet wide by 16 feet high A pathway cuts diagonally through the garden. What is the length of the pathway?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
This is a Pythagorean theorem problem. The Pythagorean theorem says that in a right triangle
the sum of the squares of each leg (legs are the short sides) is equal to the square of the
hypotenuse (the longest side of the triangle).
.
In math form we can call "a" the length of one of the legs of a right triangle, "b" the length
of the other leg, and "h" the length of the hypotenuse. The equation for the Pythagorean
theorem can then be written as:
.

.
Make a sketch of the rectangular garden. Label one side 30 feet long and the other side
16 feet long. Notice that the corner where these two sides join at a common point is the
vertex of the right angle. Now draw the diagonal line joining the two other ends of the sides.
The diagonal line represents the path. It is the hypotenuse (longest side of the triangle
that is formed by the two sides and the path.
.
Back to the Pythagorean theorem. The two given sides (one 30 feet and one 16 feet) are
the legs of the triangle. If you square each of them and add these squares the result is:
.

.
The Pythagorean theorem tells us that this sum (found by squaring each leg and adding the
two squares together) must equal the square of the hypotenuse.
.
So we can write that:
.

.
where h represents the hypotenuse or in this problem, the length of the garden path. You can
solve for h by just taking the square root of both sides of the equation to get:
.

.
and your calculator will tell you that feet
.
So h = 34 feet and that is the length of the pathway you needed to find.
.
Hope this helps you to understand the Pythagorean theorem a little and what a useful
theorem it can be.
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