Geometry Puzzle – Challenge 73

Challenge:

The perimeter of a square is 13 cm and the perimeter of an equilateral triangle is 7 cm. What is the difference of a side of the square and a side of a triangle?

A- \(\frac{7}{13}\) cm

B- \(\frac{11}{12}\) cm

C- \(1\frac{1}{4}\) cm

D- \(2\frac{1}{4}\) cm

E- \(\frac{13}{7}\) cm

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The perimeter of a square is 13cm. Therefore, one side of the square is \(\frac{13}{4}\) cm.
The perimeter of the equilateral triangle is 7cm. Therefore, one side of the triangle is \(\frac{7}{3}\) cm.
The difference of a side of the square and a side of a triangle is:
\(\frac{13}{4} – \frac{7}{3} = \frac{39-28}{12} = \frac{11}{12}\) cm

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Frequently Asked Questions

What is the perimeter of an equilateral triangle formula?

The perimeter of an equilateral triangle is P = 3s, where s is the length of one side, because all three sides are equal. Working backward, s = P ÷ 3. In this puzzle the triangle’s perimeter is 7 cm, so each side is 7/3 cm, or about 2.33 cm, which is the value subtracted from the square’s side of 13/4 cm.

What is the perimeter of an equilateral triangle with 7 cm sides?

An equilateral triangle with 7 cm sides has a perimeter of 3 × 7 = 21 cm. Notice the difference from this challenge: here the perimeter, not the side, is 7 cm, so you divide instead of multiply and get a side of 7/3 cm. Always check whether a problem gives you the side length or the total distance around.

How do you find the perimeter of a triangle and a square?

Add the lengths of all the sides. For a square, all four sides match, so P = 4s; for an equilateral triangle, P = 3s; for any other triangle, P = a + b + c. This puzzle runs the formulas in reverse: a square with perimeter 13 cm has side 13/4 cm, and the triangle with perimeter 7 cm has side 7/3 cm.

How do you find the perimeter of an equilateral triangle with the height?

Use h = (√3/2)s, so the side is s = 2h ÷ √3 and the perimeter is P = 2√3 × h. For example, if the height is 6 cm, the side is 12/√3 = 4√3 ≈ 6.93 cm and the perimeter is 12√3 ≈ 20.78 cm. For the triangle in this puzzle, side 7/3 cm, the height is about 2.02 cm.

How do you find the perimeter of an equilateral triangle if the area is given?

Start from A = (√3/4)s² and solve for the side: s = √(4A ÷ √3). Then multiply by 3. For example, if the area is 16√3 cm², then s² = 64, s = 8 cm and the perimeter is 24 cm. The triangle in this challenge, with side 7/3 cm, has an area of 49√3/36, about 2.36 cm².

What is the semi-perimeter of an equilateral triangle?

The semi-perimeter is half the perimeter, so for an equilateral triangle it is 3s/2. It shows up in Heron’s formula for area. In this puzzle the triangle’s perimeter is 7 cm, so its semi-perimeter is 3.5 cm. With side 7/3 cm, 3 × (7/3) ÷ 2 gives the same 3.5 cm.

Related Lessons You May Like

• How to find the area of rectangles
• How to find the perimeter of rectangles
• How to find the area of triangles
• How to solve systems of equations
• How to solve multi-step word problems

If your student enjoys these puzzles, Geometry for Beginners works the same relationships inside a full curriculum. Pre-Algebra for Beginners covers the algebra foundations.