Find the perimeter of the figure in radical form with the radicals simplified.
-
A) n.
D) 1080 in.

Question

Find the perimeter of the figure in radical form with the radicals simplified.
-
A) n. 
D) 1080 in.

Quizplus · Accepted Answer

The figure can be divided into two right triangles and two smaller rectangles. 
The length of the bottom rectangle is $\sqrt{75}-\sqrt{27}=4\sqrt{3}$.
The length of the top rectangle is $10-\sqrt{48}=10-4\sqrt{3}$.
The perimeter of the two rectangles combined is $2(10-4\sqrt{3}+4\sqrt{3}+4\sqrt{3})=28$.
The length of the hypotenuse of the right triangle on the left is $\sqrt{27}+10-\sqrt{48}=\sqrt{27}+6\sqrt{3}$.
The length of the hypotenuse of the right triangle on the right is $\sqrt{27}+\sqrt{75}=\sqrt{3}(4+5)=\sqrt{3}(9)$.
The perimeter of the figure is $28+ \sqrt{3}(9)+\sqrt{27}+6\sqrt{3}=\boxed{11ebb63d_1bfb_82b2_b851_457f7dda72f8_TB8475_11}$

Find the Perimeter of the Figure in Radical Form with the Radicals