Posted by Christian on Monday, May 7, 2007 at 11:34am.
The area of a rectangular blanket in square centimeters is 40x^2+2x-65. The width is 4x-5 cm^2. Find the dimensions of the blanket in terms of x.
For Further Reading
Algebra 2 - Brown, Monday, May 7, 2007 at 2:40pm
What is this question? like a foreign language or something
Could someone pleae answer this question seriously?
length*width= 40x^2+2x-65
length*(4x-5)=40x^2+2x-65
factor the right side.
divide both sides by 4x-5
To solve this problem, we need to find the dimensions of the rectangular blanket in terms of x. Let's start by considering the area of the blanket, which is given as 40x^2 + 2x - 65.
The formula for the area of a rectangle is length * width. In this case, the width is given as 4x - 5 cm^2. So, we can set up the equation:
length * (4x - 5) = 40x^2 + 2x - 65
To find the length, we need to isolate it on one side of the equation. Let's distribute the length using the distributive property:
4xl - 5l = 40x^2 + 2x - 65
Now, we have an equation in terms of length (l) and x. The right side of the equation, 40x^2 + 2x - 65, can be factored further if possible. Factoring this expression, we get:
(8x + 13)(5x - 5)
Now, let's simplify the equation:
4xl - 5l = (8x + 13)(5x - 5)
To find the value of length (l), we can divide both sides of the equation by the width (4x - 5):
(4xl - 5l) / (4x - 5) = (8x + 13)(5x - 5) / (4x - 5)
This gives us the length in terms of x:
l = (8x + 13)(5x - 5) / (4x - 5)
Similarly, we can find the value of width (w) by dividing the area (40x^2 + 2x - 65) by the length (l):
w = (40x^2 + 2x - 65) / l
So, the dimensions of the blanket in terms of x are:
Length = (8x + 13)(5x - 5) / (4x - 5)
Width = (40x^2 + 2x - 65) / (8x + 13)(5x - 5)