SOLUTION: The length of a rectangle lawn between classroom building is 2 yd less than twice the width of a lawn. A path that is 34 yd long stretches diagonally across the area. What are the
Algebra ->
Customizable Word Problem Solvers
-> Geometry
-> SOLUTION: The length of a rectangle lawn between classroom building is 2 yd less than twice the width of a lawn. A path that is 34 yd long stretches diagonally across the area. What are the
Log On
Question 1114397: The length of a rectangle lawn between classroom building is 2 yd less than twice the width of a lawn. A path that is 34 yd long stretches diagonally across the area. What are the dimensions of the lawn? Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website! The diagonal of a rectangle forms a right triangle with the sides of the rectangle. So we can use the Pythagorean Theorem to solve the problem.
If we blindly plug in numbers, the algebra would look like this:
Then use any of a number of methods of solving that equation to find the positive root.
The problem is far more easily solved if you use Pythagorean triples -- sets of 3 integers that can be the side lengths of a right triangle.
The problem says the diagonal of the rectangle is 34 yards. Not approximately 34 yards -- exactly 34 yards. Therefore we want a Pythagorean triple with the largest number 34.
34 is 2 times 17, and a common Pythagorean triple is (8,15,17). So the side lengths of the right triangle formed by the lawn and its diagonal are 16, 30, and 34.
And indeed 16 is the positive solution to that ugly quadratic equation shown above.
