Question

the floor of a shed given on the right has an area of 65 square feet. the floor is in the shape of a rectangle whose length is 3 feet less than twice the width. find the length and the width of the floor of the shed. the length of the floor of the shed is and the width is

Explanation:

Answer:

Mathematics: Algebra
Let the width be \( w \) feet. Then the length \( l = 2w - 3 \) feet.
Since the area \( A=l\times w=(2w - 3)w = 65 \), we have \( 2w^{2}-3w - 65=0 \).
Using the quadratic formula \( w=\frac{-(-3)\pm\sqrt{(-3)^{2}-4\times2\times(-65)}}{2\times2}=\frac{3\pm\sqrt{9 + 520}}{4}=\frac{3\pm\sqrt{529}}{4}=\frac{3\pm23}{4} \).
We take the positive root \( w=\frac{3 + 23}{4}=6.5 \) (since width cannot be negative).
Then \( l=2\times6.5-3=10 \).
Length: \( 10 \) feet, Width: \( 6.5 \) feet