Question

5. Given: L, M, and N are midpoints of$\Delta \text{TKO}$. Find the perimeter of each figure.

a. $\Delta \text{TKO}$

b.$\Delta \text{LMK}$

c. $▱\text{TNML}$

d. quad. $\text{LNOK}$

Short answer

a. Perimeter of $\Delta \text{TKO}$ is $\mathbf{40}$.

b. Perimeter of $\Delta \text{LMK}$ is $\mathbf{20}$.

c. Perimeter of $▱\text{TNML}$is$\mathbf{26}$

d. Perimeter of quad.$\text{LNOK}$is$\mathbf{34}$.

Step-by-step solution

a. Step 1 - Consider the diagram.

Here, L,M and N are the midpoints of sides of $\Delta TKO$.

- Show the calculation.

Perimeter of $\Delta TKO$ is:

$\begin{array}{c}\text{Perimeter}=TO+OK+KT\\ =\left(5+5\right)+\left(7+7\right)+\left(8+8\right)\\ =40\end{array}$

- State the conclusion.

Therefore, perimeter of $\Delta TKO$ is 40.

b.Step 1 - Consider the diagram.

Here, L,M and N are the midpoints of sides of $\Delta TKO$.

- Show the calculation.

Perimeter of $\Delta LMK$is:

$\begin{array}{c}\text{Perimeter}=LM+MK+KL\\ =5+7+8\\ =20\end{array}$

- State the conclusion.

Therefore, perimeter of $\Delta LMK$ is 20.

c.Step 1 - Consider the diagram.

Here, L,M and N are the midpoints of sides of $\Delta TKO$.

- Show the calculation.

Perimeter of the parallelogram $TNML$ is:

$\begin{array}{c}\text{Perimeter}=TN+NM+ML+LT\\ =5+8+5+8\\ =26\end{array}$

- State the conclusion.

Therefore, perimeter of the parallelogram $TNML$ is 26.

d.Step 1 - Consider the diagram.

Here, L,M and N are the midpoints of sides of $\Delta TKO$.

- Show the calculation.

Perimeter of quadrilateral $LNOK$ is:

$\begin{array}{c}\text{Perimeter}=LN+NO+OK+KL\\ =7+5+14+8\\ =34\end{array}$

- State the conclusion.

Therefore, perimeter of quadrilateral $LNOK$ is 34.