Question

The area of a rectangular room is 45 sq. m. If the length had
been 3 m less and the breadth 1 m more it would have been a
square. Find the length and breadth of the room. Ans: 9 m, 5 m​

Answer 1

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The area of a rectangular room is 45 sq. m. If the length had been 3 m less and the breadth 1 m more. it would have been a square. Find the length and breadth of the room.

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Let,

length of room = x metres

breadth of room = y metres

then,

as we know area of rectangle =( length × breadth)

we will get,

$\tt \: xy = 45 \: {m}^{2} \: - - eqn(1)$

it is given that,

if length will become 3 m less = (x - 3) m

and

breadth will become 1 m more =(y +1) m

then,

the figure will turn into square means

length will become equal to breadth

such that,

$\tt \: x - 3 = y + 1 \\ \\ \tt \: x = y + 4 \: - - eqn(2)$

putting x= y +4 in eqn(1)

$\tt(y + 4)(y) = 45 \\ \\ \tt \: {y}^{2} + 4y - 45 = 0$

Solving the quadratic eqn

$\tt \: {y}^{2} + 4y - 45 = 0 \\ \\ \tt \: {y}^{2} + 9y - 5y - 45 = 0 \\ \\ \tt \: y(y + 9) - 5(y + 9) = 0 \\ \\ \tt \: (y - 5)(y + 9) = 0 \\ \\ y = 5 \: and \: y = - 9$

since length cannot be negative hence we will take only

y = 5 m

putting this value in eqn(2)

x = y +4

x = 5 + 4

x = 9 m

Hence,

length of room will be 9 m.

and breadth will be 5 m.

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Answer 2

Step-by-step explanation:

in a square the length and breadth are equal