Question

Triangle KLM represents a section of a park set aside for picnic tables. The picnic area will take up approximately 400 square yards in the park.
To the nearest yard, what amount of fencing is needed to surround the perimeter of the picnic area?

95 yards
107 yards
160 yards
190 yards

Answer 1

Answer:

B. 107 yards

Step-by-step explanation:

Going off the correction in the comments of the first answer lol.

Answer 2

Given triangle KLM with two sides given as 45 yd and 20 yd and a 25 degree angle opposite the 20 yd side.

We find the angle made at the opposite of the 45 yd side using the sine rule as follows.
$\frac{\sin{A}}{a} = \frac{\sin{B}}{b} \\ \frac{\sin{25^o}}{20} = \frac{\sin{B}}{45} \\ \sin{B}= \frac{45\sin{25^o}}{20} = \frac{19.0178}{20} =0.9509 \\ B=\arcsin{(0.9509)}=71.97^o$

Thus, the third angle is given by 180 - 25 - 71.97 = 83.03 degrees.

We also use the sine rule to find the third side of the triangle as follows.
$\frac{\sin{A}}{a} = \frac{\sin{C}}{c} \\ \frac{\sin{25^o}}{20} = \frac{\sin{83.03^o}}{c} \\ c= \frac{20\sin{83.03^o}}{\sin{25^o}} = \frac{19.8522}{\sin{25^o}} =46.97 yds$

Therefore, amount of fencing needed to surround the perimeter of the picnic area = 45 + 20 + 46.97 = 111.97 ≈ 120 yds