Problemas
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
Roztwór
Elsa
professionell · Tutor durante 6 años
4.6
(231 Votos)
Respuesta
Let's denote the width of the original rectangle as
feet. Since the length is 9 feet longer than the width, the length can be expressed as
feet.The area of the original rectangle is given by:
When each feet, the new width becomes
feet and the new length becomes \( (w + 9) + 9 = w + 18 \) feet.The area of the new rectangle is:
According to the problem, the new area is 4 times the original area:
We can simplify this equation:
Since
is a common factor, we can divide both sides of the equation by
):
Solving for
:
So, the width of the original rectangle is 6 feet. The length, being 9 feet longer than the width, is:
Therefore, the size of the original rectangle is:- The width or short side is
feet.- The length or long side is
feet.