median.1. If LI = 23 and EK = 36, find NO.2. If LI= 15.5 and EK = 22.5, find NO....

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October 2022 1 7 Report

Activity 2: Median of a trapezoid

Using trapezoid LIKE with median NO, find the indicated base/median.

1. If LI = 23 and EK = 36, find NO.

2. If LI= 15.5 and EK = 22.5, find NO.

3. If NO = 19 and LI = 13, find EK.

4. If NO = 21.5 and EK = 28, find LI.

5. If LI = 3x + 8, EK = 6x + 4 and NO = 24, find LI and EK.

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TheoD

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$\underline{\mathcal{SOLUTION}}:$

1. If LI = 23 and EK = 36, find NO.

$\begin{gathered}\begin{gathered}\:\:\:\:\:\:\:\:\:\:\boxed{\begin{array}{l}\textsf { \small LI = 23, EK = 36} \\ \ \: \: \sf \small {NO = \frac{LI \: + \: EK}{2}} \\ \: \: \: \sf \small {NO = \frac{23 \: + \: 6}{2}} \\ \: \: \: \: \: \: \sf \small{NO = \frac{59}{2}} \\ \: \: \: \boxed{{ \sf \small NO = 29.5}} \end{array}} \end{gathered}\end{gathered}$

2. If LI = 15.5 and EK = 22.5, find NO.

$\begin{gathered}\begin{gathered}\:\:\:\:\:\:\:\:\:\:\boxed{\begin{array}{l}\textsf { \small LI = 15.5, EK = 22.5} \\ \ \: \: \: \: \sf \small {NO = \frac{LI \: + \: EK}{2}} \\ \: \: \: \: \sf \small {NO = \frac{12.5 \: + \: 22.5}{2}}\\ \: \: \: \: \: \: \: \boxed{{ \sf \small NO = 19}} \end{array}} \end{gathered}\end{gathered}$

3. If NO = 19 and LI = 13, find EK.

$\begin{gathered}\begin{gathered}\:\:\:\:\:\:\:\:\:\:\boxed{\begin{array}{l}\textsf { \small NO = 19, LI = 13} \\ \ \: \: \: \sf \small {NO = \frac{LI \: + \: EK}{2}} \\ \: \: \: \: \sf \small {NO = \frac{13 \: + \: EK}{2}} \\ \: \: \textsf {\small 38 = 13 \: + \: EK} \\ \: \: \: \: \: \boxed{{ \sf \small EK = 25}} \end{array}} \end{gathered}\end{gathered}$

4. If NO = 21.5 and EK = 28, find LI.

$\begin{gathered}\begin{gathered}\:\:\:\:\:\:\:\:\:\boxed{\begin{array}{l}\textsf { \small NO = 21.5, EK = 28} \\ \ \: \: \: \: \: \sf \small {NO = \frac{LI \: + \: EK}{2}} \\ \: \: \: \: \: \sf \small {21.5 = \frac{LI \: + \: 28}{2}} \\ \: \: \: \: \: \textsf {\small 43 = LI \: + \: 28} \\ \: \: \: \: \: \: \: \: \boxed{{ \sf \small LI = 15}} \end{array}} \end{gathered}\end{gathered}$

5. If LI = 3x + 8, EK = 6x + 4 and NO = 24, find LI and EK.

$\begin{gathered}\begin{gathered}\:\:\:\:\:\:\:\:\:\boxed{\begin{array}{l}\textsf{ \small LI = 3x + 8, EK = 6x + 4, NO = 24 } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \small NO = \frac{LI \: + \: EK}{2}} \\ \: \: \: \: \: \: \: \: \: \: \: \sf \small {24 = \frac{3x \: + \: 8 \: + \: 6x \: + \: 4}{2}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \small {24 = \frac{9x \: + \: 12}{2}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \textsf{ \small 48 = 9x \: + \: 12} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \textsf{\small 36 = 9x} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{{ \sf \small x = 4}} \\ \\ \sf Now, \\ \\ \: \: \: \: \: \: \: \: \: \textsf{LI = 3x + 8 = 3(4) + 8} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\boxed{ \sf \small LI = 20} \\ \\ \: \: \: \: \: \: \: \: \textsf{EK = 6x + 4 = 6(4) + 4} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \sf \small EK = 28} \end{array}} \end{gathered}\end{gathered}$

TheKeyandSolve Thank you ng marami

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