If the total area of the rectangle below is 168 square units, how long is each side? To find out how long the x side must be, use the diagram below to complete the table and answer the questions that follow. Also if you can, answer the question at the bottom of my image! I'd appreciate the help.
For a rectangle of length L and width W, the area is:
A = L*W
In this case we have:
L = x + 2
w = x
Then the area of this rectangle is:
A = (x + 2)*x = x^2 + 2*x
And we know that this area is equal to 168 square units, then:
168 = x^2 + 2*x
We can rewrite this as:
x^2 + 2*x - 168 = 0
This is a quadratic equation, and the solutions are given by Bhaskara's equation, such that for an equation of the form:
a*x^2 + b*x + c = 0
The solutions are given by:
In our case, the solutions are:
Then the two solutions are:
x = (2 - 26)/2 = -12
x = (2 + 26)/2 = 14
Notice that x is the width of the rectangle, and we can not have a negative width, so we can discard the first option.
Then we can conclude that:
x = 14
Then the width of the rectangle is 14 units long, and the length is 14 + 2 = 16 units long.
Now, how the lengths are related to eachother?
The length is 2 units longer than the width.
answer: no, but if it does it's a obvious pattern.
she should of added 9^2 and 12^2. that is because it is a^2+b^2=c^2. c^2 is the hypotenuse and should always be bigger than the other two numbers. which is why she should of added 9 squared and 12 squared together instead of 15 squared.