Answer:
We can solve this problem using a system of equations. In this system of equations, let's have X = the length and Y = the width of the rectangle in question. Given this and the information above, we can write out the following two relationships:
Equation 1: X * Y = 8 units
Equation 2: X - 7 = Y
We can draw these two relationships based upon the area data given for the rectangle and the relationship between the width and length. Plugging the value of Y from equation 2 into equation 1, we can isolate one variable, X, and solve for it:
X * (X - 7) = 8. Substituted equation 1
X^2 - 7X = 8 After being multiplied-out
0 = X^2 - 7X - 8 After moving all terms to one side of the equation
0 = (X - 8) * (X + 1) After factoring the equation
X = 8, -1 Solve for X by finding an X that would make the equation true (equal to 0)
Now that we have solved for X, we have to possibilities for what X could be, however a length cannot be negative and this tells us that it must be 8 units, the other option. Plugging the value for X back into the original equation 2, we solve for Y:
Equation 2: X - 7 = Y → 8 - 7 = Y = 1
Now that we see that Y = 1 units, we can check our solution by plugging it back into the area equation established earlier:
Equation 1: X * Y = 8 units
Because X = 8 and Y = 1, this equation is satisfied and we know that we have the correct result.
Final answer: width = 1 unit, length = 8 units
Step-by-step explanation:
hope it helps
Length of the given rectangle is 8 units
Given that;
Width of rectangle = (Length - 7) units
Area of rectangle = 8 square units
Find:
Length of rectangle
Computation:
Assume;
Length of rectangle = a
So,
Width of rectangle = (Length - 7) units
Width of rectangle = (a - 7) units
Area of rectangle = l × b
8 = a × (a - 7)
a² - 7a = 8
a² - 7a - 8 = 0
a² - (8 - 1)a - 8 = 0
a² - 8a +a - 8 = 0
a(a - 8) + 1(a - 8) = 0
(a - 8)(a - 1) = 0
So,
a = 8 and a = 1
So,
Length of rectangle = 8 units
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