Liam has a rectangular backyard. He measured one side of the yard and found it to be 85 feet and its diagonal to be 117 feet. Determine, to the nearest 10th of a foot, the length of the other side of his backyard.
We are told in the question that Liam’s backyard is rectangular. The length of one of the sides of the yard is 85 feet. We are told that the length of the diagonal is 117 feet. We are asked to calculate the length of the other side of the rectangular yard.
The diagonal has created a right-angled triangle. We know that in any right triangle we can use the Pythagorean theorem. This states that 𝑎 squared plus 𝑏 squared is equal to 𝑐 squared, where 𝑐 is the length of the longest side of the triangle known as the hypotenuse.
Substituting in the values from this question, we have 𝑥 squared plus 85 squared is equal to 117 squared. We can subtract 85 squared from both sides so that 𝑥 squared is equal to 117 squared minus 85 squared. The right-hand side of this equation simplifies to 6464. We can then square root both sides of this equation. As 𝑥 must be positive, 𝑥 is equal to 80.3990 and so on.
We are asked to give our answer to the nearest 10th of a foot. This is the same as rounding to one decimal place. The length of the other side of Liam’s backyard is therefore equal to 80.4 feet to the nearest 10th of a foot.