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What is the length of the diagonal of a rectangle-shaped box through the size of

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Explanation:

To solve this trouble we need an extension of the Pythagorean Theorem:

So the equation to solve becomes

So the street of the diagonal line is

.Explanation:

The length of the diagonal line is from the bottom left hand corner closest to united state to the optimal right hand edge that"s farthest away from us.

This kind of a trouble may seem to it is in a small more complex than it really is.

In order to settle for the diagonal line length, all that"s forced is the Pythagorean Theorem. This equation will certainly be supplied twice to solve for the dashed line.

For the first step the this problem, it"s beneficial to imagine a triangle "slice" that"s being taken within the prism.

, whereby the diagonal of interest is D2, and also D1 is the diagonal that cuts from corner to edge of the bottom challenge of the prism. Of this triangle that"s outlined in pink dashed lines, the provided information (the size of the prism) provides a length for among the legs (16).We can already "map out" that D2 (the hypotenuse of the dashed triangle) have the right to be addressed by making use of the Pythagorean theorem if us can obtain the length of the other leg (D1).

The following step that this difficulty is to resolve for D1. This will certainly be the very first use of the Pythagorean theorem. D1 is the diagonal of the base and also is minimal to a 2D face. This can be represented as:

The hypotenuse the the base, or the an enig length leg of the dashed triangle, can be resolved by making use of the Pythagorean Theorem:

Now that us calculated the size of D1, D2 have the right to be addressed for by making use of the Pythagorean organize a 2nd time: