Example

Finding the Dimensions of a Rectangular Sign with Area 3030 Square Feet

Apply the geometry problem-solving strategy to find the dimensions of a rectangular sign when its area is 3030 square feet and the length is one foot more than the width. Let ww represent the width, making the length w+1w + 1. Substitute these expressions into the area formula A=lwA = l \cdot w to obtain 30=(w+1)w30 = (w + 1)w. Distribute to get 30=w2+w30 = w^2 + w, and subtract 3030 from both sides to rewrite the equation in standard form as 0=w2+w300 = w^2 + w - 30. Factor the quadratic expression into (w+6)(w5)=0(w + 6)(w - 5) = 0 and apply the Zero Product Property to find w=6w = -6 or w=5w = 5. Because a physical dimension must be positive, discard 6-6. The width is 55 feet, and the length is 5+1=65 + 1 = 6 feet.

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Updated 2026-04-30

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