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

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
RELATED QUESTIONS
A farmer wishes to put a diagonal brace on his gate. How long should the brace be if the... (answered by nerdybill,unlockmath)
The diagonal brace on a gate is 5 feet long. THe height of the gate is 4 feet long. How... (answered by checkley77)
MERRIC IS BUYING A BOARD TO USE AS A DIAGONAL BRACE ON A RECTANGULAR GATE. THE GATE IS 36 (answered by checkley75)
A carpenter added a diagonal brace to a gate that measures 45 inches wide and 55 inches... (answered by fractalier)
the gate of a fence is 8ft. tall and 15ft. wide. how long is the diagonal strip (d) used... (answered by vleith)
A carpenter wants to build a diagonal brace for a rectangular gate that is 5 feet wide... (answered by Cromlix)
Diagonal brace. The width of a rectangular gate is 2 meters (m) larger than its height.... (answered by jojo14344)
Diagonal brace. The width of a rectangular gate is 2 meters (m) larger than its height.... (answered by nerdybill)
Diagonal brace. The width of a rectangular gate is 2 meters (m) larger than its height.... (answered by nyc_function)