Question

Length of a rectangle is 4x²+12x and the area of the rectangle is 24x⁴+72x³, what is the width of the rectangle?

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Answer 1

The width of rectangle is
`6x^2`

Solution:

Given that,

`\text{Length of rectangle } = 4x^2+12x`

`\text{Area of rectangle } = 24x^4+72x^3`

To find: width of rectangle

The area of rectangle is given by formula:

`\text{Area of rectangle } = length * width`

Therefore, width is given as:

`width = \frac{\text{Area of rectangle}}{length}`

Substituting the given values we get,

`width = (24x^4+72x^3)/(4x^2+12x)`

Factor out 24 and
`x^3` from numerator

`width = (24x^3(x+3))/(4x^2+12x)`

Factor out 4 and x from denominator

`width = (24x^3(x+3))/(4x(x+3))`

Cancel the common terms in numerator and denominator

`width = 6x^2`

Thus the width of rectangle is
`6x^2`