The length of a rectangle is 9 feet longer than it is wide. If each side is increased 9 feet, then the area is multiplied by 4 . What was the size of the original rectangle? The width or short side is square feet The length or long side is square feet

Let's denote the width of the original rectangle as \( w \) feet. Since the length is 9 feet longer than the width, the length can be expressed as \( w + 9 \) feet.<br /><br />The area of the original rectangle is given by:<br />\[ \text{Area} = \text{length} \times \text{width} = (w + 9) \times w \]<br /><br />When each feet, the new width becomes \( w + 9 \) feet and the new length becomes \( (w + 9) + 9 = w + 18 \) feet.<br /><br />The area of the new rectangle is:<br />\[ \text{New Area} = (\text{new length}) \times (\text{new width}) = (w + 18) \times (w + 9) \]<br /><br />According to the problem, the new area is 4 times the original area:<br />\[ (w + 18) \times (w + 9) = 4 \times (w + 9) \times w \]<br /><br />We can simplify this equation:<br />\[ (w + 18)(w + 9) = 4(w + 9)w \]<br /><br />Since \( w + 9 \) is a common factor, we can divide both sides of the equation by \( w +assuming \( w + 9 \neq 0 \)):<br />\[ w + 18 = 4w \]<br /><br />Solving for \( w \):<br />\[ 18 = 3w \]<br />\[ w = 6 \]<br /><br />So, the width of the original rectangle is 6 feet. The length, being 9 feet longer than the width, is:<br />\[ w + 9 = 6 + 9 = 15 \]<br /><br />Therefore, the size of the original rectangle is:<br />- The width or short side is \( 6 \) feet.<br />- The length or long side is \( 15 \) feet.