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bezimeni [28]
3 years ago
13

the length of a rectangle is five feet less than its width. If the area of the rectangle is 84 square feet, find its dimensions

Mathematics
1 answer:
KIM [24]3 years ago
6 0
Let
x---------> the length of the rectangle
y--------> the width of the rectangle

we know that
A=84 ft²
[area of rectangle]=x*y-----> 84=x*y-----> equation 1
x=y-5------> equation 2
substitute 2 in 1
84=[y-5]*y-----> 84=y²-5y---------> y²-5y-84=0

using a graph tool-----> to resolve the second order equation
see the attached figure

the solution is
y=12
x=y-5-----> x=12-5-----> x=7

the answer is
the length of the rectangle is 7 ft
the width of the rectangle is 12 ft

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-------------------------------------------

So in summary so far
M = 64
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The shortest side is opposite the smallest angle. The side MP is opposite the smallest angle N = 48

The longest side is going to be opposite the largest angle. In this case, side MN is opposite the largest angle P = 68

The medium side is opposite the medium angle. So NP is the medium side length

-------------------------------------------------------

Final Answers:
Shortest Side = MP
Medium Side = NP
Longest Side = MN
See the attached image for a visual summary

The ascending order would be: MP, NP, MN

Note: Something like MP is the same as PM. The order of endpoints for any given individual segment doesn't matter

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