L = 2W-5
L * W = 75
Substitute 2W-5 for L in second equation and solve for W. Insert that value into the first equation and solve for L. Check by inserting both values into the second equation.
L * W = 75
Substitute 2W-5 for L in second equation and solve for W. Insert that value into the first equation and solve for L. Check by inserting both values into the second equation.
Step 1: Let's assume the width of the rectangle as 'w' feet.
Step 2: According to the given information, the length of the rectangle is 5 feet less than twice its width. Therefore, the length can be expressed as 2w - 5 feet.
Step 3: The formula for the area of a rectangle is length × width. We know that the area of the rectangle is 75 square feet. So, we can set up the equation:
(2w - 5) × w = 75
Step 4: Simplify the equation:
2w^2 - 5w = 75
Step 5: Rearrange the equation to have a quadratic equation form:
2w^2 - 5w - 75 = 0
Step 6: Factorize the quadratic equation:
(2w + 15)(w - 5) = 0
Step 7: Set each factor equal to zero and solve for 'w':
2w + 15 = 0 or w - 5 = 0
Step 8: Solve for 'w' in each equation:
w = -15/2 or w = 5
Since the width cannot be negative, we discard the solution w = -15/2.
Step 9: The width of the rectangle is 5 feet.
Step 10: To find the length, substitute the width value into the expression for the length:
length = 2w - 5
length = 2(5) - 5
length = 10 - 5
length = 5
Therefore, the length of the rectangle is 5 feet.