Question

Haruki has a piece of wire that is $24$ centimeters long. He wants to bend it to form each of the following shapes, one at a time.

A regular hexagon with side length $5$ cm.

A square of area $36$ cm².

A right triangle whose legs are $6$ and $8$ cm long.

Which of the shapes can Haruki make?

Triangle only

Hexagon and square only

Hexagon and triangle only

Square and triangle only

Hexagon, triangle, and square

Video solution:

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Written solution:

The regular hexagon would have perimeter $6\cdot5=30$ , too long for the wire. The square has side length $6$ , so its perimeter is $24$ . The right triangle has hypotenuse $10$ , so its perimeter is $6+8+10=24$ . Haruki can make the square and the triangle only.

2026 AMC 8 Problem 3

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Problem 3 in Other Years