the lenght of a rectangleis 6 inches more than its width. The area of the rectangle is 91 square inches. Find the dimensions of the rectangle
length is 13 inches
width is 7 inches
let width and length both be x;
(x+6) [this is length] & (x) [this is width];
(x+6) * x = 91;
x^2+6x = 91;
x^2 + 6x - 91 = 0;
solve by factoring;
(x-7)(x+13)= 0
x = 7 & x = -13 (-13 is not real)
check;
L=(7+6)
W= 7
(7+6)*7=91
Width = W.
Length = W+6.
A = L*W = (W+6)W = W^2+6W = 91.
W^2+6W-91 = 0. -91 = -7*13. sum = -7+13 = 6 = B.
(W-7)(W+13) = 0
W = 7 and -13.
w = 7 in.
L = W+6 = 7+6 = 13 in.
To find the dimensions of the rectangle, we can set up an equation based on the information given.
Let's assume the width of the rectangle is "w" inches. According to the problem, the length of the rectangle is 6 inches more than its width, so the length would be "w + 6" inches.
We can use the formula for the area of a rectangle to set up an equation:
Area = Length × Width
Given that the area of the rectangle is 91 square inches, we can substitute the values into the equation:
91 = (w + 6) × w
Now, let's solve this equation step-by-step to find the dimensions of the rectangle:
1. Expand the equation:
91 = w^2 + 6w
2. Move all terms to one side of the equation to make it equal to zero:
w^2 + 6w - 91 = 0
3. Factorize the quadratic equation:
(w + 13)(w - 7) = 0
4. Set each factor equal to zero and solve for "w":
w + 13 = 0 or w - 7 = 0
5. Solve for "w":
If w + 13 = 0, then w = -13 (We can ignore this negative value for width)
If w - 7 = 0, then w = 7
Therefore, the width of the rectangle is 7 inches.
6. Substitute the value of "w" into the expression for the length:
Length = w + 6 = 7 + 6 = 13
Therefore, the dimensions of the rectangle are 7 inches by 13 inches.
To solve this problem, we can use two variables to represent the dimensions of the rectangle. Let's use "l" to represent the length and "w" to represent the width.
According to the problem, the length of the rectangle is 6 inches more than its width, so we can write the equation:
l = w + 6 (Equation 1)
The area of a rectangle is given by the formula:
Area = length * width
In this case, the area of the rectangle is given as 91 square inches. So we can write the equation:
91 = l * w (Equation 2)
Now, let's solve these two equations simultaneously to find the values of the length and width of the rectangle.
Substituting Equation 1 into Equation 2, we get:
91 = (w + 6) * w
Expanding the equation:
91 = w^2 + 6w
Rearranging the equation and setting it equal to zero:
w^2 + 6w - 91 = 0
Now, we can solve this quadratic equation. We can either use factoring or the quadratic formula.
Using factoring:
(w - 7)(w + 13) = 0
So, either w - 7 = 0 or w + 13 = 0
If w - 7 = 0, then w = 7
If w + 13 = 0, then w = -13
Since the dimensions of the rectangle cannot be negative, we can ignore the second solution.
Therefore, the width of the rectangle is w = 7.
Substituting this value back into Equation 1, we can find the length:
l = w + 6
l = 7 + 6
l = 13
So, the dimensions of the rectangle are width = 7 inches and length = 13 inches.