Question

The rectangle below has an area of x^2-11x+30 Square meters in a length of x-5 meter. What expression represents the width of the rectangle

Answer 1

Answer:

We have been given that the area of a rectangle is x^2-11x+30x

2

−11x+30 square meters and a length of (x-5)(x−5) meters.

Since the area of a rectangle is product of its width and length.

\text{Area of rectangle}=\text{Width of rectangle*Length of rectangle}Area of rectangle=Width of rectangle*Length of rectangle

We can find width of our rectangle by dividing area of rectangle by length of rectangle.

\text{Width of rectangle}=\frac{\text{Area of rectangle}}{\text{Length of rectangle}}Width of rectangle=

Length of rectangle

Area of rectangle

Let us substitute our given values in above formula.

\text{Width of rectangle}=\frac{x^2-11x+30}{x-5}Width of rectangle=

x−5

x

2

−11x+30

Let us factor out numerator by splitting the middle term.

\text{Width of rectangle}=\frac{x^2-6x-5x+30}{(x-5)}Width of rectangle=

(x−5)

x

2

−6x−5x+30

\text{Width of rectangle}=\frac{x(x-6)-5(x-6)}{(x-5)}Width of rectangle=

(x−5)

x(x−6)−5(x−6)

\text{Width of rectangle}=\frac{(x-6)(x-5)}{(x-5)}Width of rectangle=

(x−5)

(x−6)(x−5)

Upon cancelling out x-5 from numerator and denominator we will get,

\text{Width of rectangle}=(x-6)Width of rectangle=(x−6)

Therefore, the expression (x-6)(x−6) meters represents width of the rectangle.

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