Question

Can someone please answer this thanks

Answer 1

I believe the answer is B

Answer 2

Answer:

D

Step-by-step explanation:

If not for the triangle carved out, this figure would just be a regular rectangle with an easy-to-calculate perimeter. However, you now need to find the perimeter of two sides of this triangle and replace that for the perimeter that the rectangle would have taken up. The first step is to find out how long AC is. Since FE and AD have the same length, the difference between FE and CD must be AC, or 10-7=3 units. Now, imagine the line AC still being there, forming triangle ABC. Angle CAB can be found easily, by subtracting 30 from the known right angle in the corner of the rectangle to get 60 degrees. Similarly, you can find angle ACB with the knowledge that angles DCB and ACB are linear pairs, meaning that they add up to 180 degrees. 180-120=60, making that the angle measurement of ACB. Finally, you know that angle ABC is also 60 degrees, because the interior angles of a triangle always add up to 180 degrees and 180-60-60=60. This means that triangle ABC is equilateral, and that all of the sides have the same length. Since you know that AC has length 3, AB and BC also must have length 3. You can subtract the new length from the old length to get an extra 3 units in the perimeter. Now you can calculate the perimeter of the rectangle as usual. 8+10+8+10+3=39 units, or answer choice D. Hope this helps!