Question

Find the perimeter of a equilateral
triangle whose area is equal to the
of a triangle with side 21 cm
16 cm, 13 am
Answer corrects to 2
decimal place.​

Answer 1

Answer:

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High School Math : How to find the perimeter of an equilateral triangle

Study concepts, example questions & explanations for High School Math

Example Questions

High School Math Help » Geometry » Plane Geometry » Triangles » Equilateral Triangles » How to find the perimeter of an equilateral triangle

Find The Perimeter Of An Equilateral Triangle : Example Question #1

Gre11

A square rug border consists of a continuous pattern of equilateral triangles, with isosceles triangles as corners, one of which is shown above. If the length of each equilateral triangle side is 5 inches, and there are 40 triangles in total, what is the total perimeter of the rug?

The inner angles of the corner triangles is 30°.

Possible Answers:

200

124

188

180

208

Correct answer:

188

Explanation:

There are 2 components to this problem. The first, and easier one, is recognizing how much of the perimeter the equilateral triangles take up—since there are 40 triangles in total, there must be 40 – 4 = 36 of these triangles. By observation, each contributes only 1 side to the overall perimeter, thus we can simply multiply 36(5) = 180" contribution.

The second component is the corner triangles—recognizing that the congruent sides are adjacent to the 5-inch equilateral triangles, and the congruent angles can be found by

180 = 30+2x → x = 75°

We can use ratios to find the unknown side:

75/5 = 30/y → 75y = 150 → y = 2''.

Since there are 4 corners to the square rug, 2(4) = 8'' contribution to the total perimeter. Adding the 2 components, we get 180+8 = 188 inch perimeter.

Step-by-step explanation: