Question

The sum of the perimeters of a square and an equilateral triangle is equal 1 point to the perimeter of a rectangle whose dimensions are 15"x 21". The area of the square is 81 sq. in. The length of a side of the equilateral triangle is ____.

Answer 1

To find the length of the side of the equilateral triangle, we need to work with the given information step by step. Start by finding the side length of the square, then find the perimeter of the rectangle. Finally, subtract the perimeter of the square from the perimeter of the rectangle to find the perimeter of the equilateral triangle.

Step-by-step explanation:

To find the length of the side of the equilateral triangle, we need to work with the given information step by step. Let's start by finding the length of the side of the square.

Since the area of the square is given as 81 square inches, we can find the side length by taking the square root of 81, which is 9 inches. The perimeter of the square is then 4 times the side length, which is 36 inches.

Next, let's find the perimeter of the rectangle. The perimeter is the sum of the lengths of all four sides. Since the dimensions of the rectangle are given as 15 inches by 21 inches, the perimeter is 2 times the sum of 15 and 21, which is 72 inches.

Now, we are given that the sum of the perimeters of the square and the equilateral triangle is equal to the perimeter of the rectangle.

Therefore, the perimeter of the equilateral triangle can be found by subtracting the perimeter of the square from the perimeter of the rectangle. So the perimeter of the equilateral triangle is 72 - 36 = 36 inches.