geometry

[vaibhav101]

An umbrella 50 inches long can lie on the bottom of a trunk whose length and width in inches can be:

A 26 and 30
B 34 and 36
C 31 and 31
D 40 and 21
E 40 and 30

[Vincen]

Hello.

Here, we have to imagine the trunk as a rectangle, and we want to find its dimensions such that a 50 inches long umbrella can lie on it. If one of the sides of the rectangle (length or width) would be 50, then the umbrella would lie parallel to the respective side.

But, in the given options, all dimensions are lesser than 50. Therefore, we have to calculate the length of the diagonals of each given rectangle (the diagonal is the largest distance between two points of a rectangle).

The length of each diagonal is $$\left(A\right)\ D=\sqrt{26^2+30^2}\approx39.69\ $$ $$\left(B\right)\ D=\sqrt{34^2+36^2}\approx49.51$$ $$\left(C\right)\ D=\sqrt{31^2+31^2}\approx43.84$$ $$\left(D\right)\ D=\sqrt{40^2+21^2}\approx45.17$$ $$\left(E\right)\ D=\sqrt{40^2+30^2}=50.$$ As we can see, the umbrella can lie just in the last rectangle.

Therefore, the correct answer is the option E.

I hope it can help you.

[Jeff@TargetTestPrep]

An umbrella 50 inches long can lie on the bottom of a trunk whose length and width in inches can be:

A 26 and 30
B 34 and 36
C 31 and 31
D 40 and 21
E 40 and 30

We need the diagonal of the trunk to be at least 50 inches. We know that the length, width and diagonal of the trunk obey the Pythagorean theorem, that is, L^2 + W^2 = D^2. Since D = 50, D^2 = 2500. So we need L^2 + W^2 ≥ 2500. Skimming through the answer choices, we see choice E will work since 40^2 + 30^2 is exactly 50^2.

Answer: E