the diagonal of a square splits the rectangle into two 30-60-90 triangle if the diagonal is 10 centimeters find the area of the rectangle answer

Answer 1

This questions is testing your knowledge of 30-60-90 triangles. A 30-60-90 triangle is an equilateral triangle split in half so the sides have the relationship x, 2x, x(square root of 3) You can use Pythagoras theorem to verify this

The diagonal is the hypotenuse of the triangle making it the longest side so 10 = 2x in your case and x = 5

and the area of your rectangle would be 5 (5 square root of 3) = 25 sq rt 3

Answer 2

Use trigonometry to solve for the 2 sides of the triangle. One will be 10 x sin(3) and the other will be 10 cos (30). Which yields 5 and 5 x sqrt(3)

Area = l x w = 25(sqrt(3))