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n200080 [17]
3 years ago
6

The line segments of a cube include edges, the diagonals of the faces, and the diagonals through the interior of the cube. Which

is the longest? Which is the shortest? Explain.
Mathematics
2 answers:
Ksenya-84 [330]3 years ago
0 0

They diagonal through the interior of the cube is the longest. The hypotenuse is the longest side of a right triangle. The diagonal of the cube is the hypotenuse of a right angle with legs that are diagonal of a face and an edge. The edges are the shortest. They are legs of a right triangle with the diagonal of a face as the hypotenuse.


nata0808 [166]3 years ago
0 0

Answer:

The diagonal through the interior of the cube is the longest. The hypotenuse is the longest side of a right triangle. The diagonal of the cube is the hypotenuse of a right triangle with legs that are the diagonal of a face and an edge. The edges are the shortest. They are legs of a right triangle with the diagonal of a face as the hypotenuse.

Step-by-step explanation:its the sample response

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One side of a kite is 8 cm less than four times the length of another side. The perimeter of the kite is 78 cm. Find the lengths
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Answer:

9.4\:\mathrm{cm},\\9.4\:\mathrm{cm},\\29.6\:\mathrm{cm},\\29.6\:\mathrm{cm}

Step-by-step explanation:

A kite consists of two pairs of congruent adjacent sides. Therefore, we have the following equation:

2x+2(4x-8)=78, where x is the length of the shorter sides.

Solving, we get:

2x+8x-16=78,\\10x=94,\\x=\fbox{$9.4\:\mathrm{cm}$}.

Plugging in x=9.4 into 4x-8, we get:

4(9.4)-8,\\37.6-8,\\\fbox{$29.6\:\mathrm{cm}$}.

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