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Oduvanchick [21]
3 years ago
10

The length of a rectangle is 4 units less than the width. The area of the rectangle is 21 units. What is the length, in units, o

f the rectangle?
Mathematics
1 answer:
bazaltina [42]3 years ago
4 0

The formula of an area of a rectangle:

A = wl

We have l = w - 4 and A = 21.

Substitute:

w(w - 4) = 21       <em>use distributive property</em>

(w)(w) + (w)(-4) = 21

w² - 4w = 21     <em>subtract 21 from both sides</em>

w² - 4w - 21 = 0

w² - 7w + 3w - 21 = 0

w(w - 7) + 3(w - 7) = 0

(w - 7)(w + 3) = 0 ↔ w - 7 = 0 ∨ w + 3 = 0

w = 7 ∨ w = -3 < 0

l = w - 4 → l = 7 - 4 = 3

<h3>Answer: the length = 3 u.</h3>
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