Question

42. A parallelogram and a square have the same area. If the sides of the
square measure 40 m and altitude of the parallelogram measures 25 m,
find the length of the corresponding base of the parallelogram.
bomb​

Answer 1

Answer:

side of square = 40m

Area of square = S× S=40×40= 1600sq.m

alt. of parallelogram=25m

Area of parallelogram = Area of square

B×H = 1600

B×25 = 1600

B = 1600/25

B = 64m

Answer 2

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✺Answer:

♦️GiveN:

• 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:-

$\large{ \rm{ \odot\: area \: of \: square \square \: = (side) {}^{2}}} \\ \\ \large{ \rm{ \odot\: area \: of \: parrallelogram = base \times}} \\ \large{ \rm{ \: \: \: \: \: \: \: \: \: \:\:\:\:corresponding \: altitude}}$

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

$\large{ \rm{ \rightarrow \: (side) {}^{2} = base \times corresponding \: height}}$

Putting the given values,

$\large{ \rm{ \rightarrow \:( 40) {}^{2} \: \: {m}^{2} = base \times 25 \:m}} \\ \\ \large{ \rm{ \rightarrow \: base = \frac{40 \times 40}{25} \: m}} \\ \\ \large{ \rm{ \rightarrow \: base = \cancel{\frac{1600}{25}m}}} \\ \\ \large{ \rm{ \rightarrow \: base = 64 \: m}} \\ \\ \large{ \therefore{ \boxed{ \rm{ \purple{corresponding \: base = 64m}}}}}$

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✺In the attachment

• Diagram of Required square and parallelogram for better understanding.

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