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Difficulty: MediumPerimeter and Area of 2D Figures

A kite designer is creating a kite in the shape of a rhombus. The two crossing wooden dowels that form the internal diagonals of the kite measure 1616 inches and 3030 inches. What is the total perimeter of the kite's outer edge, in inches?

Answer: 68 inches

Answer

68
The correct answer is found by recognizing that a rhombus's diagonals bisect each other perpendicularly. This allows the use of the Pythagorean theorem with half-diagonal lengths (88 and 1515) to find a side length of 1717. Multiplying this single side length by the four equal sides of the rhombus yields a total perimeter of 6868 inches.

Step-by-Step Solution

1
Determine the properties of the diagonals in a rhombus.
The diagonals bisect each other at right angles, forming four identical right triangles.
This breaks down the rhombus into simpler geometric shapes (right triangles), allowing for side length calculation.
2
Calculate the lengths of the legs for one of the right triangles.
The legs are 88 inches (16÷216 \div 2) and 1515 inches (30÷230 \div 2).
The diagonals cut each other exactly in half at the intersection.
3
Use the Pythagorean theorem to find the length of the rhombus's outer edge.
The side length is 82+152=64+225=289=17\sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17 inches.
The outer edge forms the hypotenuse of the right triangle created by the half-diagonals.
4
Calculate the total perimeter.
17×4=6817 \times 4 = 68 inches.
A rhombus has four equal sides, so the total perimeter is four times the length of one side.

Key Concept

Perimeter of a Rhombus and Pythagorean Theorem
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Topics

Perimeter and Area of 2D Figures

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