Question 1199532
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Answer: <font color=red>3 cm by 7 cm rectangle</font>
3*7 = 21


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Explanation:


Let's list the ways to factor 21 with positive values:
1*21 = 21
3*7 = 21


The gap from 3 to 7 is 4 units, because 7-3 = 4, so it's fairly clear that we have a 3 by 7 rectangle.


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Another approach using algebra.


x = width
x+4 = length which is four units larger than the width


area = length*width
area = (x+4)*x
area = x^2+4x


We'll set this equal to the stated area 21 square cm, and solve for x.


x^2+4x = 21
x^2+4x-21 = 0


From here you can factor like so
x^2+4x-21 = 0
(x-3)(x+7) = 0
x-3 = 0 or x+7 = 0
x = 3 or x = -7
Ignore x = -7 because it makes no sense to have a negative length or width.


If x = 3, then x+4 = 3+4 = 7
We arrive at 3*7 = 21 to confirm the answers.


Another way to solve x^2+4x-21 = 0 is to use the quadratic formula.
We have
a = 1
b = 4
c = -21
to get the following steps:
{{{x = (-b+-sqrt(b^2-4ac))/(2a)}}}


{{{x = (-4+-sqrt((4)^2-4(1)(-21)))/(2(1))}}}


{{{x = (-4+-sqrt(100))/(2)}}}


{{{x = (-4+-  10)/(2)}}}


{{{x = (-4+10)/(2)}}} or {{{x = (-4-10)/(2)}}}


{{{x = (6)/(2)}}} or  {{{x = (-14)/(2)}}}


{{{x = 3}}} or  {{{x = -7}}}
Then as mentioned earlier, we ignore the negative x value and have x = 3 lead to x+4 = 7.
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