Question

A diagonal of a rectangle is 8 mm and forms with one side an angle measuring 30. Find the area of the rectangle. ( Hint: The diagonal creates a 30-60 right triangle. )

Answer 1

A diagonal of a rectangle is 8cm and forms an angle measuring 30 with one side. Find the area of a rectangle

Let's first draw the picture. The diagonal of your rectangle will be a line that goes from the top left corner of your rectangle to the bottom right corner. This line is the hypotenuse of your RIGHT triangle. The problem tells us that the hypotenuse forms a 30 degree angle with on of the sides. We can pick either side, but I chose to pick the side that includes the left side of the rectangle. Now, we have a 30-60-90 right triangle. The base of the triangle is opposite the 30 degree angle, so it will equal x. The hypotenuse is 2x and the height is x√3.

 

SO, since we know the hypotenuse is 8cm, we know: 8=2x and x=4;  x√3=4√3

 

The area of a rectangle is b*h, so we multiple 4√3*4 to give us 16√3

 

Hope that helps!