SOLUTION: The width if a triangle is fixed at 13cm. What lengths will make the perimeter greater than 88cm? Although I initially thought this solution could be easy, I am second guessing mys

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Question 208494: The width if a triangle is fixed at 13cm. What lengths will make the perimeter greater than 88cm? Although I initially thought this solution could be easy, I am second guessing myself. My thought process feels me the answer could be 30cm since the perimeter would be 90. IDK-I've been struggling w/ Algebra & geometry for weeks now. Is there an easy way to fibnd the right solution? TY-Angel
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
The width if a triangle is fixed at 13cm. What lengths will make the perimeter greater than 88cm? Although I initially thought this solution could be easy, I am second guessing myself.
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Let the lengths of the unknown sides be x and y.
Then x + y + 13 > 88
So x + y > 75
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There is another condition.
In order to have a triangle the sum of any two sides must be greater
than the 3rd side.
So x+13 > y
and
y +13 > x
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Rearranging these three inequalities you get:
y > -x + 75
y < x+ 13
y > x - 13
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Graph these three boundaries:

Shade the half-plane above y > -x+75
Shade the half-plane below y < x+13
Shade the half-plane above y > x-13
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Find the intersection of y = x+13 with y = -x+75: (31,44)
Find the intersection of y = x-13 with y = -x+75: (44,31)
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Solution:
31 31 where x + y = 75
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Cheers,
Stan H.
Send any response to this to stanbon@comcast.net as the feedback
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