# the area of a room is 65 1/4m² .if its breadth is 5 7/6m ,what is it’s length​

the area of a room is 65 1/4m² .if its breadth is 5 7/6m ,what is it’s length​

1. ## $$\rm\red{ANSWER\:❣}$$

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$$\tt\begin{gathered} let \: breadth \: be \: x \\ then \: the \: length \: will \: be \: (x + 4) \\ area \: of \: rectange = l \times b \\ l = (x + 4) = {x}^{2} + 4x \\ b = (x – 4) \\ (x – 4)(x + 10) \\ x(x + 10) – 4(x + 40) \\ ( {x}^{2} + 10x)( – 4x – 40) \\ {x}^{2} + (10x – 4x) – 40 \\ {x}^{2} + 6x – 40 \\ therefore \: {x}^{2} + 4x = {x}^{2} + 6x – 40 \\ 4x = 6x – 40 \\ 6x – 4x = 40 – 2x = 40 \\ x = \frac{40}{2} \\ breadth = 20m \\ length = 24m \\ area = l \times b \\ = (20 \times 24) {m}^{2} \\ = 480 {m}^{2} \end{gathered}$$

2. ## CorrectQuestion:

• The area of a room is 65 1/4m² . If it’s breadth is 5 7/16m.what is it’s length

• Length of room is 12m

## Given:

• Area of room is 65 1/4 m²
• Breadth of room is 5 7/16m

## Tofind:

• Length of room

## Solution:

》Area of room = 65 1/4 m²

》4(65) + 1 / 4

》261/4 m

Area of room is 261/4 m

》Breadth of room is 5 7/16 m

》16(5) + 7 / 16

》87/16 m

Now , we have to find the length of room

• Let the length be l

As we know that,

• Area of room = l × b

Where , l is length and b is breadth

》Area of room = l × b

》261/4 = l × 87/16

》l = 261/4 × 87/16

》l = 12m

Hence , Length of room is 12m