A parallelogram and a square have the same area. If the sides of the square measure 56cm and altitutde of the parallelogram measures 128 cm, find the length of the corresponding base of the parallelogram.
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Answers
Answer:
A parallelogram and square has equal area.
Side of Square = 40 m
Altitude of Parallelogram = 25 m
♦️To FinD:
Length of corresponding base of the parallelogram.
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✺Explanation of Q.
According to question, Area of parallelogram and square are same. We know that Area of these two figures are:-
\begin{gathered} \large{ \rm{ \odot\: area \: of \: square \square \: = (side) {}^{2}}} \\ \\ \large{ \rm{ \odot\: area \: of \: parrallelogram = base \times}} \\ \large{ \rm{ \: \: \: \: \: \: \: \: \: \:\:\:\:corresponding \: altitude}} \end{gathered}⊙areaofsquare□=(side)2⊙areaofparrallelogram=base×correspondingaltitude
We have, the area same. Side of square is given, altitude of parallelogram given, So we can easily find the corresponding base by just applying the above formula.
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✺Solution:
Area of Square = Area of Parallelogram
\large{ \rm{ \rightarrow \: (side) {}^{2} = base \times corresponding \: height}}→(side)2=base×correspondingheight
Putting the given values,
\begin{gathered}\large{ \rm{ \rightarrow \:( 40) {}^{2} \: \: {m}^{2} = base \times 25 \:m}} \\ \\ \large{ \rm{ \rightarrow \: base = \frac{40 \times 40}{25} \: m}} \\ \\ \large{ \rm{ \rightarrow \: base = \cancel{\frac{1600}{25}m}}} \\ \\ \large{ \rm{ \rightarrow \: base = 64 \: m}} \\ \\ \large{ \therefore{ \boxed{ \rm{ \purple{corresponding \: base = 64m}}}}} \end{gathered}→(40)2m2=base×25m→base=2540×40m→base=251600m→base=64m∴correspondingbase=64m
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✺In the attachment
Diagram of Required square and parallelogram for better understanding.