Subjects algebra

Lot Dimensions

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Lot Dimensions


1. **Stating the problem:** Amar wants to find the dimensions (length and width) of a rectangular lot. The perimeter is 2300 feet. 2. **Identify variables:** Let the length be $x$ feet. 3. The width is 350 feet longer than the length, so width = $x+350$ feet. 4. **Using the perimeter formula:** $$P = 2(\text{length} + \text{width})$$ Given $$P = 2300$$, substitute: $$2300 = 2(x + x + 350)$$ 5. **Simplify the equation:** $$2300 = 2(2x + 350)$$ $$2300 = 4x + 700$$ 6. **Solve for $x$:** $$4x = 2300 - 700$$ $$4x = 1600$$ $$x = \frac{1600}{4} = 400$$ 7. **Calculate the width:** $$x + 350 = 400 + 350 = 750$$ 8. **Answer:** The dimensions of the lot are length = 400 feet and width = 750 feet, represented as the ordered pair $(400,750)$.