108k views
0 votes
19) The area in square feet of a rectangular carpet is x^2- 17x+30 Find the dimensions for the

expressions of the length and the width.​

User Bogdanw
by
4.5k points

1 Answer

4 votes

Answer:

The dimensions are x-15 and x-2.

Explanation:

The formula for the area of a rectangle is A = l x w, where l is length and w is width.

The area is found by multiplying two numbers OR expressions that represent the length and the width.

If the area is x² - 17x + 30, factoring this will give two expressions for length and width.

When factoring, first check if there is a common factor other than 1 between all of the variables. There is no common factor for this.

We can factor using decomposition.

x² - 17x + 30

Write out the factors for the first and last terms:

Since the middle number is a negative, the right side factors should be negative also.

1 -30 -15 -10 -6

1 -1 -2 -3 -5

To find the correct pair of factors, the pairs multiplied diagonally from each side then added together should give the middle number, -17. (The first term's correct factors can only be 1 and 1).

The correct pairing is:

1 -15

1 -2

(1 x -15) + (1 x -2) = -17

The factors for factored form are found by adding brackets around the terms.

(1 -15)

(1 -2)

x² - 17x + 30 = (x - 15)(x - 2)

Apply the area formula A = (l) (w).

The dimensions are x-15 and x-2.

User Melkor
by
5.3k points