The diagonal of a rectangle are 24 inches long intersect at an angle of 60°.Find the perimeter of the rectangle.Pls help me.

make a sketch drawing both diagonals

Look at one of the triangles containing the 60° angle.
Since the diagonals bisect each other, each side containing the 60° angle must be 12 inches long.
The triangle must be isosceles, so each of the other angles is also 60°, and it is also equilateral.
So one side of the rectangle is 12 and its diagonal is 24
No look at one of the large triangles with the diagonal as its hypotenuse, it has angles 30-60-90°
so it is in the ratio of 1 : √3 :2
Our triangle is in the ratio of 12 : x : 24
so x = 12√3

perimeter = 2(12√3) + 2(12)
= 24√3 + 24 inches

To find the perimeter of the rectangle, we need to know the length and the width of the rectangle. Let's denote the length as L and the width as W.

Since the diagonals of a rectangle intersect at a right angle, we can use the Pythagorean theorem to find the relationship between the length, width, and diagonal. In this case, we are given the length of the diagonal, which is 24 inches, and the angle between the diagonals, which is 60 degrees.

Using the Pythagorean theorem, we can set up the following equation:

L^2 + W^2 = (24/2)^2

Simplifying:

L^2 + W^2 = 12^2
L^2 + W^2 = 144

Now, we need to solve this equation to find the length and width. However, there are infinite possible solutions, as any combination of L and W that satisfies this equation would be a valid rectangle. Without additional information, we cannot determine the exact values of L and W.

Once you have the values of L and W, the perimeter of the rectangle can be calculated by using the formula:

Perimeter = 2L + 2W

Substitute the values of L and W into this equation, and you will find the perimeter of the rectangle.