[tex]\underline{\mathcal{QUESTION}}:[/tex]
In parallelogram HOME, find the value of each unknown variables and the length of the indicated sides.
[tex]\underline{\mathcal{SOLUTION}}:[/tex]
In parallelogram,
diagonals bisects each other
opposite sides are equal
[tex]\mathcal{SOLUTION\:OF\:NO.\:1\:AND\:2}[/tex]
[tex]\begin{array}{| c | c | c }\sf \: HS = SM & \sf \: ES = OS\\ \sf \: 3x = 12 & \sf y + 2 = 2y - 6\\ \sf \: x = \frac {12}{3} & \sf 2 + 6 = 2y - y \\ \sf \: x = 4 & \sf y = 8\end{array}[/tex]
[tex]\mathcal{SOLUTION\:OF\:NO.\:3}[/tex]
[tex]\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{l} \: \: \: \: \: \: \sf \small OH = EM \\ \\ \: \: \: \: \: \: \: \sf \small OH = 30 \\ \\ \sf \small Therefore,EM = 30\end{array}}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}[/tex]
[tex]\mathcal{SOLUTION\:OF\:NO.\:4}[/tex]
Diagonals are equal,
[tex]\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{l}\sf \small EO = ES + OS \\ \\ \: \sf \small y + 2 + 2y - 6 \\ \\ \: \: \: \: \: \: \sf \small 3y - 4 \\ \\ \: \: \: \sf 3(12)-4 \\ \\ \: \: \: \: \: \sf 36 - 4 \\ \\ \: \: \: \: \: \: \: \: \: \sf 32\end{array}}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}[/tex]
[tex]\mathcal{SOLUTION\:OF\:NO.\:5}[/tex]
As diagonals are equal,
[tex]\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{l} \: \: \: \: \sf \small EO = HM \\ \\ \sf \small 32 = EO = HM \\ \\ \: \: \: \: \: \sf \small HM = 32\end{array}}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}[/tex]
[tex]\underline{\mathcal{ANSWER}}:[/tex]
[tex]\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{l} \sf \small 1. \: x = 4 \: \: \: \: \: \: \: \: \: \\ \\ \sf \small 2. \: y = 8 \: \: \: \: \\ \\ \sf \small 3. \: \overline{EM} = 30 \\ \\ \sf \small 4. \: \overline{EO} = 32 \\ \\ \sf \small 5. \: \overline{HM} = 32 \end{array}}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}[/tex]
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