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abruzzese [7]
3 years ago
9

The length of a rectangle is five less than its width. The area of the rectangle is 84 square feet. Write a quadratic equation i

n standard form, ax^2+bx+c=0
Mathematics
1 answer:
salantis [7]3 years ago
4 0

<u>Given</u>:

The length of a rectangle is 5 less than its width.

The area of the rectangle is 84 square feet.

We need to determine the quadratic equation in standard form that represents the area of the rectangle.

<u>Dimensions of the rectangle:</u>

Let l denote the length of the rectangle.

Let w denote the width of the rectangle.

Since, it is given that the length is 5 less than its width, it can be written as,

l=5-w and w=w

<u>Area of the rectangle:</u>

The area of the rectangle can be determined using the formula,

A=length \times width

Substituting A = 84, l=5-w and w=w, we get

84=(5-w)\times w

84=5w-w^2

Adding both sides of the equation by w², we have;

w^2+84=5w

Subtracting by 5w on both sides, we get;

w^2-5w+84=0

Thus, the quadratic equation in standard form for the area of the rectangle is w^2-5w+84=0

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