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
B
14m2
C
11m2
D
21m2

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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