SOLUTION: 1.) A farmer wishes to put a diagonal brace on his gate. How long should the brace be if the gate is rectangular, 12 by 5 ft? 2.) A trunk is 4 x 3 x 2 ft. What is the longest r

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Question 254063: 1.) A farmer wishes to put a diagonal brace on his gate. How long should the brace be if the gate is rectangular, 12 by 5 ft?
2.) A trunk is 4 x 3 x 2 ft. What is the longest rod that this truck can contain?
Found 2 solutions by richwmiller, oberobic:
Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!

Answer by oberobic(2304) (Show Source):
You can put this solution on YOUR website!
Both questions rely on the Pythagorean formula: c^2 = a^2 + b^2.
.
The diagonal brace on the gate would be the hypotenuse of a right triangle with a=12 and b=5.
a^2 = 144
b^2 = 25
so
c^2 = 169
By inspection we see that is a perfect square: sqrt(169) = 13.
That means the brace must be 13 ft.
.
The longest rod that can fit in a trunk will fit in three dimensions, for example, from the lower left front corner to the upper right back corner.
The height of the triangle will be one of known dimensions.
We are told 4x3x2, so we have to assume these are length by width by height.
a^2 = height^2 = 2^2 = 4
The other leg of the triangle the rod defines will be the diagonal of the base of the trunk.
The base of the trunk is a rectangle that is 4x3, so the diagonal will be 5.
b^2 = base^2 = 5^2 = 25
c^2 = 4 + 25 = 29
c = sqrt(29) = 5.385