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2 years ago

4. The length of a rectangle is one more than twice the width. The area is 105 in?.

Mathematics

1 answer:

Zanzabum2 years ago

7 0

9514 1404 393

Answer:

7 in

Step-by-step explanation:

For width w in inches, the length is given as 2w+1. The area is the product of length and width, so we have ...

A = LW

105 = (2w +1)w

2w^2 +w -105 = 0

To factor this, we're looking for factors of -210 that have a difference of 1.

-210 = -1(210) = -2(105) = -3(70) = -5(42) = -6(35) = -7(30) = -10(21) = -14(15)

So, the factorization is ...

(2w +15)(w -7) = 0

Solutions are values of w that make the factors zero:

w = -15/2, +7 . . . . . negative dimensions are irrelevant

The width of the rectangle is 7 inches.

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