Question

The area of a rectangle is 50ft , and the length of the rectangle is 5 ft less than three times the width. Find the dimensions of the rectangle.

Answer 1

We know from the problem that l = 3w - 5. We also know the formula for area is A = w * l. Therefore, the area of the rectangle is A = w * (3w - 5). We can then set this equation equal to 50 as the question states and solve for w.

`50 = w * (3w-5)`

Expand the multiplication

`50 = 3w^(2)- 5w`

Subtract 50 from both sides.

`0 = 3w^(2) - 5w - 50`

We now have a quadratic equation and can solve it using the quadratic formula to find w. We find that the solutions to the equation are 5 and -3.3. We know that the width can't be negative, so the width must be 5.

Finally, we can plug this solution into the length formula we found earlier to solve for length.

`l = 3w - 5`

Plug in the solution to w.

`l = 3(5) - 5`

Multiply 3 and 5.

`l = 15-5`

Subtract 5

`l = 10`

Therefore the width is 5 and the length is 10.