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Referring to the figure, if area of square $1$ is $16$ square units, area of square $2$ is $48$ square units, then what is the area of square $3$ in sq. units?

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56

sq. units

64

sq. units

78

sq. units

96

sq. units

answer is B.

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Detailed Solution

Given, referring to the figure, area of square

1

16

square units, area of square

2

48

square units.
Question Image

Area of the square 1 =

sid e^{2}

= 16

\Rightarrow

Side = 4 units
Area of the square 2 =

sid e^{2}

= 48

\Rightarrow

Side =

\sqrt{48}

units
The triangle formed in between three squares becomes a right angled triangle since the angles of a square are right angles.
Therefore side of square

3

can be written as

\sqrt{(4)^{2} + (\sqrt{48})^{2}}

\Rightarrow

Side of square

3

= \sqrt{16 + 48}

\Rightarrow

Side of square

3

= 8

units
Area of a square is

sid e^{2}

\Rightarrow

Area of square 3 =

8^{2} = 64

sq.units.
Hence, option 2 is correct.

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Referring to the figure, if area of square 1is 16 square units, area of square 2 is 48 square units, then what is the area of square 3 in sq. units?

Detailed Solution

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Referring to the figure, if area of square $1$ is $16$ square units, area of square $2$ is $48$ square units, then what is the area of square $3$ in sq. units?