Asked by J
The diagonal of a rectangle are 24 inches long intersect at an angle of 60°.Find the perimeter of the rectangle.Pls help me.
Answers
Answered by
Reiny
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
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
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