SOLUTION: the length of a rectangle is 5 less than the width. the area is 36 square inches. find the length and width.

Question 824427: the length of a rectangle is 5 less than the width. the area is 36 square inches. find the length and width.

Found 2 solutions by TimothyLamb, FightinBlueHens:
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
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x = length
y = width
x = y - 5
xy = 36
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xy = 36
(y - 5)y = 36
yy - 5y - 36 = 0
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the above quadratic equation is in standard form, with a=1, b=-5, and c=-36
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
1 -5 -36
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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this quadratic has two real roots (the x-intercepts), which are:
y = 9
y = -4
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negative width doesn't make sense for this problem, so use the positive root:
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answer:
x = length = 4 in
y = width = 9 in
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---
Solve quadratic equations, quadratic formula:
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---
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Answer by FightinBlueHens(27) (Show Source): You can put this solution on YOUR website!
Area = length * width --> A = l * w
the length is 5 less than the width so l = w - 5
Area = w * (w-5)
36 = w * (w-5)
What two numbers that are multiplied together give you 36 that are 5 units apart?

w = 9 (because it is the larger side)
l = 4 (because it is the shorter side)
OR
w^2 - 5w -36 = 0
Use the quadratic formula:
w = (5+-sqrt((-5)^2-4*1*-36))/2*1
w = (5+-sqrt(25+144))/2
w =(5+-sqrt(169))/2
w = (5+-13)/2
w = 18/2 = 9 OR w = -8/2 = -4
w is a length so it cannot be negative. w is therefore 9. This answer works because if w is 5 greater than the length, the length is 4, and 9 * 4 = 36.
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