High School

If the area of a rectangle is [tex]15x^{4} + 21x^{3} - 12x^{2}[/tex] and the width is [tex]3x^{2}[/tex], what is the length?

Answer :

Final answer:

The length of the rectangle is 5x^2 + 7x - 4.

Explanation:

In this mathematics problem, the length of a rectangle is to be found. Given is that the area of the rectangle, 15x^(4)+21x^(3)-12x^(2), and the width is 3x^(2). We know that the area of the rectangle is the product of its length and width. So, to find the length, we divide the area by the width.

That gives us:

Length = (15x^(4)+21x^(3)-12x^(2)) / 3x^(2).

After simplifying this, we get:

Length = 5x^(2) + 7x - 4. So, the length of the rectangle is 5x^2 + 7x - 4.

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