Question

A farmer is building a pen inside a barn. The pen will be the shape of a right triangle. The farmer has 14 feet of barn wall to use for one side of the pen and wants another side of the pen to be 15 feet long.

a) How many different lengths for the third side are possible? Explain.

b) To the nearest tenth of a foot, find all possible lengths for the third side of the triangle. Show your work.

c) The farmer wants the area of the pen to be as large as possible. What length should he choose for the third side? Justify your answer.

Answer 1

d) Find the measure of the acute angles for the triangle you described in part (c). Round to the nearest degree.

Answer 2

@ganeshie8 @phi @iGreen @Legends

Answer 3

@Callisto

Answer 4

My questions on these are more rhetorical so if somebody could just help me interpret the question thanks

Answer 5

@YesThisIsDog

Answer 6

Hi, for the first one, is it asking for all measures possible no matter if it is a right triangle or not? Or what is it asking for.

Answer 7

I sure hope it has to be a right triangle :P
Otherwise, there'd be infinitely many possible lengths for the third side :D

Answer 8

well they give 2 sides so it would be 1<x<29 if they're talking about all measures possible no matter if it is a right triangle or not

Answer 9

Very good. But it'll take an eternity to consider all those sides (LOL) so let's just go with the problem which already states from the beginning that the triangle must be a right triangle. Given that, how many possible lengths for the third side are there? It's not infinite anymore :)

Answer 10

But wouldn't that be B? See thats what confuses me.