The combined perimeter of an equilateral triangle and square is 10 cm. Find the dimensions of triangle and square that produce the minimum total area

Solution:

Given combined perimeter of an equilateral triangle and a square is 10

The perimeter of triangle + perimeter of square = 10

Let the side of the triangle and the side of the square be 'a' units

We know perimeter of equilateral triangle is 3a

Perimeter of a square is 4a

So, 3a + 4a = 10

7a = 10

a = 10/7

Now, area of triangle is √3/2 a²

Area of a square is a²

Sum = √3/2 a² + a²

Sum = √3/2(10/7)² + 10²/7²

Sum = 12.37 + 0.20

Sum = 12.57

Therefore, total area is 12.57 sq units

---

The combined perimeter of an equilateral triangle and square is 10 cm. Find the dimensions of triangle and square that produce the minimum total area

Summary:

The combined perimeter of an equilateral triangle and square is 10 cm, the dimensions of triangle and square that produce the minimum total area is side = 10/7