Math Problem of the Week - Algebra and Up - Apr. 24, 2022 to Apr. 30, 2022

Algebra and Up: 

Question: A dog run is three times as long as it is wide. If its perimeter is 104 feet, what is the area of the dog run? 

Answer: 507 square feet

Solution: We can represent the relationship between the width and length of the dog run with the equation 3W = L. We can also know that 2 times the width plus 2 times the length of a rectangle is its perimeter, so 2W + 2L = 104. We solve for the length and the width by substituting 3W for L in the second equation, which makes 2W + 6W = 8W = 104. From there, we can find that the width is 13 feet, so the length must be 39 feet. The area is therefore 13 × 39 = 507 feet.