Question

Julian installed a total of 10 yards of fence which runs along the perimeter of his square garden. He decides to run a watering hose between two opposite corners. What length of hose will he need, to the nearest tenth of a yard?

Solution

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Step 1

1 of 2

First, we find the side length ss of the square using the given perimeter of 10 yards:

P=4sP=4s

10=4s10=4s

2.5 yards=s2.5\text{ yards}=s

The length of the hose, xx, will be the diagonal of the square which is the hypotenuse of the right triangle formed:

s2+s2=x2s^2+s^2=x^2

2.52+2.52=x22.5^2+2.5^2=x^2

12.5=x212.5=x^2

x=12.5x=\sqrt{12.5}

To the nearest tenth of a yard,

x3.5 yardsx\approx \color{#c34632}3.5\text{ yards}

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