Question

1. maries office is rectangular in shape and has an area of 250 square feet. the width of the office is (2x + 5) feet and the length is (3x - 1) feet. write a quadratic equation that represents this situation.

○ x² - 13x - 250 = 0
○ 5x² + 17x - 255 = 0
○ 6x² - 13x - 255 = 0
○ 6x² + 13x - 255 = 0

Explanation:

Step1: Recall area formula for rectangle

The area $A$ of a rectangle is given by $A = length\times width$. Here, length $l=(3x - 1)$ and width $w=(2x + 5)$, and $A = 250$. So, $(3x - 1)(2x+5)=250$.

Step2: Expand the left - hand side

Using the FOIL method, $(3x - 1)(2x + 5)=3x\times2x+3x\times5-1\times2x - 1\times5=6x^{2}+15x-2x - 5=6x^{2}+13x - 5$.

Step3: Set up the quadratic equation

We have $6x^{2}+13x - 5 = 250$. Subtracting 250 from both sides gives $6x^{2}+13x-5 - 250=0$, which simplifies to $6x^{2}+13x - 255 = 0$.

Answer:

$6x^{2}+13x - 255 = 0$