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Q.

If one side of a square is represented by $18 x - 20$ and the adjacent sides are represented by $42 - 13 x$ , find the area of the square.

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a

256 square unit

b

156 square unit

c

216 square unit

d

200 square unit

answer is A.

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Detailed Solution

Concept- In wellknown a square is a parallelogram with all sides equal, adjacent aspects are perpendicular and opposite facets are parallel to every other. For this reason first we equate the given facet to locate the fee of x and then we are able to discover the cost of the side of the square by the use of the calculated cost of x.
To find the location, we multiply the bottom and peak for a parallelogram, in the case of a rectangular. Both base and height are the same. So we can do aspect.× aspect.
The sides of the square are

18 x - 20

and

42 - 13 x

. in keeping with the definition of the rectangular, all four sides of the square are equal.
Question Image

Question Image

So we are able to equate two facets of a rectangular.
Hence, it can be written as

\Rightarrow 18 x - 20 = 42 - 13 x

On collecting like terms

\Rightarrow 18 x + 13 x = 42 + 20

\Rightarrow 31 x = 62

\Rightarrow x = 2

At

x = 2

, value of

18 x - 20

is calculated below

\Rightarrow 18 \times 2 - 20

\Rightarrow 36 - 20 \Rightarrow 16

At

x = 2

, value of

42 - 13 x

\Rightarrow 42 - 13 \times 2

\Rightarrow 42 - 26

\Rightarrow 16

If the aspect of the square is a then location(A) of the rectangular is

\Rightarrow A = a \times a \Rightarrow A = a^{2}

in the given question the side of the square is sixteen.
Required area is

\Rightarrow A = {(16)}^{2} \Rightarrow A = 256 square units .

Hence, the correct option is 1.

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