The area of a rectangular blanket in square centimetersis 40x^2+2x-65. The width is 4x-5cm^2. Find the dimensions of the blanket in terms of x.
To find the dimensions of the blanket in terms of x, we need to factorize the given area formula and width expression.
Given:
Area of the blanket = 40x^2 + 2x - 65
Width of the blanket = 4x - 5
First, let's factorize the area formula 40x^2 + 2x - 65.
To factorize, we need to find two numbers that multiply to give -65 and add up to 2.
The factors of 65 are -1 and 65, -5 and 13.
-5 + 13 = 8, which is not equal to 2.
So, we check the other pair of factors: -1 and 65.
-1 + 65 = 64, which is equal to 2.
Therefore, we can write the area formula as:
40x^2 + 2x - 65 = (5x - 13)(8x + 5)
Next, let's substitute the width expression 4x - 5 into the factored form of the area formula.
Area = Width * Length
Substituting the width expression:
(5x - 13)(8x + 5) = (4x - 5) * Length
Now we can equate the corresponding terms:
5x - 13 = 4x - 5
To solve for x, we isolate the variable on one side:
5x - 4x = -5 + 13
x = 8
Now that we have found the value of x, we can substitute it back into the expressions to find the dimensions.
Width = 4x - 5
Width = 4(8) - 5
Width = 32 - 5
Width = 27 cm
Length = 8x + 5
Length = 8(8) + 5
Length = 64 + 5
Length = 69 cm
Therefore, the dimensions of the rectangular blanket in terms of x are:
Width = 27 cm
Length = 69 cm