a rectangular parking lot has a perimeter of 820 ft. the area of the parking lot measures 42,000 ft². what…

a rectangular parking lot has a perimeter of 820 ft. the area of the parking lot measures 42,000 ft². what is a dimension of the parking lot?\n120 ft\n205 ft\n210 ft\n375 ft

a rectangular parking lot has a perimeter of 820 ft. the area of the parking lot measures 42,000 ft². what is a dimension of the parking lot?\n120 ft\n205 ft\n210 ft\n375 ft

Answer

Explanation:

Step1: Set up equations

Let the length be (l) and the width be (w). Perimeter formula: (2(l + w)=820), so (l + w = 410), then (l=410 - w). Area formula: (lw = 42000).

Step2: Substitute and solve

Substitute (l = 410 - w) into (lw = 42000): ((410 - w)w=42000) (410w-w^{2}=42000) (w^{2}-410w + 42000=0) Factor: ((w - 120)(w - 350)=0) So (w = 120) or (w = 350). If (w = 120), then (l=410 - 120=290). If (w = 350), then (l=410 - 350 = 60).

Answer:

A. 120 ft