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26 votes
26 votes
Will a 12-inch ruler fit in a box that is a right rectangular prism with a width of

5 inches, a length of 10 inches, and a height of 3 inches? Explain your answer

User Bikas
by
2.9k points

1 Answer

15 votes
15 votes

Answer:

The Ruler won't fit.

Explanation:

Remark

The way this is traditional done is to find the hypotenuse of 5 and 10 inches and use this result with the height. If that does not work, then other combinations can be used.

Hypotenuse (10 and 5 )

Formula

c^2 = a^2 + b^2

Givens

a = 10

b = 5

Solution

c^2 = 10^2 + 5^2 Expand

c^2 = 100 + 25 Add

c^2 = 125

Now use the Pythagorean Theorem a second time.

z^2 = x^2 + y^2

x^2 = 125

y^2 = 3^2

z^2 = 125 + 9

z^2 = 134

This is not large enough. A ruler is 12 inches long which would mean that z^2 should come to 144. I don't think any other combination is going to do much better.

In fact looking at it more closely all combinations will give z^2 = 134.

User Dakov
by
2.7k points