Question

How do I solve for question number 6

Answer 1

Answer:

$18 + 18\sqrt{3}$

Step-by-step explanation:

The rectangle has been split into two right triangles. The hypotenuse of the triangle (the diagonal) is 18. The angle in the triangle is 30. All right triangles have unique relationships between their sides depending on the angles. This triangle must be a 30 - 60 - 90 triangle and its sides will be a scaled version of $1 - \sqrt{3} -2$.

The side 2 correspond to the hypotenuse of length 18. 2*9 = 18 and so the scale factor is 9. To find the remaining sides, multiply each side length by 9 from $1 - \sqrt{3} -2$.

It becomes $9 - 9\sqrt{3}-18$. So the rectangle is 9 by $9\sqrt{3}$.

The perimeter of the rectangle is $9 + 9 + 9\sqrt{3} + 9\sqrt{3}=18 + 18\sqrt{3}$