The length of a rectangle is 5 ft more than the width. If the area of the rectangle is 36 sq. ft what are the dimensions of the rectangle?
(Please provide steps/explanation to solve this problem.)
Let d length be y and the width be y-5 .y times y-5 =36.y times y-5 minus 36=0.then factorise
The answers are-4 and 9.to check 9(9-5)=36 or -4(-4-5)=36
Let's assume the width of the rectangle is x ft.
According to the problem, the length of the rectangle is 5 ft more than the width, so the length would be x + 5 ft.
The formula for the area of a rectangle is length × width. Therefore, we have:
Area = length × width
36 = (x + 5) × x
To solve for x, we can simplify the equation by expanding the brackets:
36 = x^2 + 5x
Now, let's rearrange the equation to solve for x:
x^2 + 5x - 36 = 0
To factorize the quadratic equation, we need to find two numbers that multiply to give -36 and add up to 5. These numbers are 9 and -4:
(x + 9)(x - 4) = 0
Now, we can set each factor equal to zero and solve for x:
x + 9 = 0 or x - 4 = 0
x = -9 or x = 4
Since the width cannot be negative, we discard x = -9.
Therefore, the width of the rectangle is x = 4 ft.
Since the length is 5 ft more than the width, the length is x + 5 = 4 + 5 = 9 ft.
So, the dimensions of the rectangle are 4 ft (width) and 9 ft (length).
To find the dimensions of the rectangle, we can set up two equations using the given information.
Let's assume the width of the rectangle is "w" feet.
According to the problem, the length of the rectangle is 5 feet more than the width. So, the length of the rectangle can be expressed as "w + 5" feet.
To find the area of the rectangle, we use the formula length multiplied by width:
Area = length × width
Given that the area is 36 sq. ft, we can write the equation as:
36 = (w + 5) × w
Now, let's solve this equation step by step:
1. Distribute the w variable to both terms inside the parentheses:
36 = w × w + 5 × w
2. Simplify:
36 = w^2 + 5w
3. Rearrange the equation so that it is in the form of a quadratic equation:
w^2 + 5w - 36 = 0
4. This quadratic equation can be factored as:
(w - 4)(w + 9) = 0
5. Set each factor equal to zero:
w - 4 = 0 or w + 9 = 0
6. Solve for the width:
w = 4 or w = -9
Since the width cannot be negative, we discard the negative solution.
Therefore, the width of the rectangle is 4 feet.
To find the length, we substitute the value of w into the expression we got earlier: w + 5.
Length = 4 + 5 = 9 feet
So, the dimensions of the rectangle are 4 feet by 9 feet.