SOLUTION: Green Leaf Landscaping is planting a rectangular wildflower garden with a perimeter of 6m and a diagonal of sqrt5 m. Find the dimensions of the garden

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Question 137052: Green Leaf Landscaping is planting a rectangular wildflower garden with a perimeter of 6m and a diagonal of sqrt5 m. Find the dimensions of the garden
Answer by solver91311(24713) About Me  (Show Source):
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The perimeter is P=2L%2B2W and we know that is equal to 6. Half of the perimeter is 3, but that is also 3=P%2F2=L%2BW. Knowing that L%2BW=3 we can write L=3-W

We also know that L, W, and the diagonal of the rectangle form a right triangle, so:

L%5E2%2BW%5E2=%28sqrt%285%29%29%5E2

But since L=3-W:

%283-W%29%5E2%2BW%5E2=5

Just expand the binomial, collect like terms, put the equation into standard form, and solve the quadratic for W. L follows directly from knowing W. Hint: The quadratic factors easily.