3. Liam has a rectangular back
yard. 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 tenth of a foot, the length
of the other side of his back yard

Length of the other side of the backyard is 80.4 feet.

Step-by-step explanation:

Let the dimensions of the Liam's rectangular backyard = 85 feet × a feet

Diagonal of the rectangle, AD = 117 feet

When we apply Pythagoras theorem in ΔABD,

AD² = AB² + BD²

(117)² = (85)² + BD²

a² = 13689 - 7225

a = √6464

  = 80.399 feet

a ≈ 80.4 feet

Therefore, length of the other side of the backyard is 80.4 feet.