# Geometry

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

1. 👍 0
2. 👎 0
3. 👁 238
1. 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

1. 👍 0
2. 👎 0

## Similar Questions

1. ### math

The diagonal of a TV set is 26 inches long. Its length is 14 inches more than the height. Find the dimensions of the TV set.

2. ### math

A semi-circle sits on top of a rectangle to form the figure below. Find its area and perimeter. Use for 3.14. The rectangle is 4 inches long and 3 inches wide. The semi-circle sits on top of the rectangle on a side that is 4

3. ### geometry

The longer diagonal of a parallelogram measures 62 cm and makes an angle of 30 degrees with the base. Find the area of the parallelogram if the diagonals intersect at angle of 70 degrees.

A picture frame is 12 inches long and 9 inches wide. In inches, what is the diagonal length of the picture frame? A)12 inches B)15 inches*** C)8 inches D)6 inches Which number is a perfect cube? A)3 B)15 C)64*** D)567 When adding

1. ### math

an architect wants to draw a rectangle with a diagonal of 13 inches.the length of the rectangle is to be 2 inches more thn twice the width.what dimensions should she make the triangle. (a)set up an equation: (b)solve the equation:

2. ### Algebra

A rectangle is drawn so the width is 7 inches longer than the height. If the rectangle's diagonal measurement is 46 inches, find the height.

3. ### geometry

The diagonal of a rectangle is 25 meters long makes an angle of 36° with one side of the rectangle. Find the area and the perimeter of the parallelogram.

4. ### Math

The description of a TV is based upon the diagonal length. If the height of a TV is 24 inches and the width is 32 inches, what is the TV's diagonal length? A) 3 B) 4 C) 21 D) 40 How do i find the diagonal length?

1. ### Geometry

TV screens are measured on the diagonal. If we have a TV-cabinet that is 72 inches long and 64 inches high, how large a TV could we put in the space (leave 2-inches on all sides for the edging of the TV)? Round your answer to the

2. ### Math

A SIDE AND A DIAGONAL OF A PARALELOGRAM ARE 12 INCHES AND 19 INCHES RESPECTIVELY. THE ANGLE BETWEEN THE DIAGONALS, OPPOSITE THE GIVEN SIDE IS 124 DEGREES. FIND THE LENGTH OF THE OTHER DIAGONAL

3. ### math

The length of a rectangle is 2 inches more than twice its width. If the perimeter of the rectangle is 34 inches, find the dimensions of the rectangle

4. ### Trigonometry

Two circles, whose radii are 12 inches and 16 inches respectively, intersect. The angle between the tangents at either of the points of intersection is 29'30'. Find the distance between the centers of the circles.