Question

select the correct answer. lmn is an isosceles triangle. what is the approximate length of side lm, and what is the approximate perimeter of triangle lmn? round your answer to the nearest tenth. a. the approximate length of side lm is 6 units, and the approximate perimeter of triangle lmn is 22.8 units b. the approximate length of side lm is 6 units, and the approximate perimeter of triangle lmn is 22.8 units c. the approximate length of side lm is 6.4 units, and the approximate perimeter of triangle lmn is 22.8 units d. the approximate length of side lm is 6.4 units, and the approximate perimeter of triangle lmn is 22 units

Explanation:

Step1: Use distance formula

For two - points $(x_1,y_1)$ and $(x_2,y_2)$, $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Let $L(1,1)$ and $M(5,-3)$. Then $LM=\sqrt{(5 - 1)^2+(-3 - 1)^2}=\sqrt{16 + 16}=\sqrt{32}\approx5.7\approx6$.

Step2: Assume base $MN$ length

Let $N(-4,-3)$ and $M(5,-3)$, $MN=|5-(-4)| = 9$.

Step3: Calculate perimeter

Since it's isosceles, perimeter $P=2LM+MN$. $P = 2\times6+9=21\approx22$.

Answer:

D. The approximate length of side LM is 6.4 units, and the approximate perimeter of triangle LMN is 22 units