CPM Homework Help : INT3 Problem 7-109

What are the area and perimeter of $ΔABC$ below? Give both exact answers and approximate (decimal) answers.

Triangle A,B,C, with dashed segment from to vertex, b, perpendicular to side, A C, labeled, 5. Angle, A, labeled 45 degrees. Angle, C, labeled 30 degrees.

Hint:

The height creates two special right triangles. What are the $45^\circ-45^\circ-90^\circ$ and $30^\circ-60^\circ-90^\circ$ triangle patterns?

More Help:

The length of the hypotenuse of a $30^\circ-60^\circ-90^\circ$ triangle is twice the side opposite the 30 degree angle. The hypotenuse of a $45^\circ-45^\circ-90^\circ$ triangle is $\sqrt{2}$ times the length of one of the legs.