Question

The tri county schools are participating in a renaissance faire. The team from Appleton High school has designed a pennant to fly over its team tent.The pennant is in the shape of a triangle. The longest side is 3 inches longer than half the middle length side. If the team captain bought 72 of satin edging for the banner , and there were 4 inches left over after the pennant was made , what are the dimensions of the pennant?

Answer 1

let the shortest side be a, let the middle side be b, then the longest side is
b/2 + 3.
so the perimeter is a + b + b/2 + 3
then a+b+b/2+3 + 4 = 72
a = 65 - 3b/2

but b/2+3 is said to be the longest side, so
b/2 + 3 > b
b + 6 > 2b
b < 6

let b = 2, then a = 62 , other side is 4 , no such triangle is possible
let b = 4, then a = 59, other side is 5, no such triangle

let b = 30, then a = 20, other side is 18
This does form a triangle, but 18 comes from the definition of the "longest" side. This is a contradiction. The same would be true for all b > 6

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