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Question

If length of a rectangle is 5 less than 3 times it's breath and perimeter of the rectangle is 22m, then area of the rectangle is: 


A
28m2
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B
14m2
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C
11m2
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D
21m2
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Solution

The correct option is A 28$$m^{2}$$
Let $$l$$ and $$b$$ be the length and breadth of rectangle.
According to the question-
$$l = 3b - 5 ..... \left( 1 \right)$$
Perimeter of rectangle $$= 22 \; m \; \left( \text{Given} \right)$$
As we know that the perimeter of rectangle is given as-
$$P = 2 \left( l + b \right)$$
Therefore,
$$2 \left( l + b \right) = 22$$
$$l + b = 11$$
$$\left( 3b - 5 \right) + b = 11 \; \left( \text{from } \left( 1 \right) \right)$$
$$4b = 11 + 5$$
$$\Rightarrow b = \cfrac{16}{4} = 4 \; m$$
Substituting the value of $$b$$ in $${eq}^{n} \left( 1 \right)$$, we have
$$l = 3 \times 4 - 5 = 7 \; m$$
Therefore,
Area of rectangle $$= l \times b = 7 \times 4 = 28 \; {m}^{2}$$
Hence the area of rectangle is $$28 \; {m}^{2}$$.

Mathematics

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