#### 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

Verified#### Step 1

1 of 2First, we find the side length $s$ of the square using the given perimeter of 10 yards:

$P=4s$

$10=4s$

$2.5\text{ yards}=s$

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

$s^2+s^2=x^2$

$2.5^2+2.5^2=x^2$

$12.5=x^2$

$x=\sqrt{12.5}$

To the nearest tenth of a yard,

$x\approx \color{#c34632}3.5\text{ yards}$

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