Question

The length of a rectangular room is 2 feet less than twice the width. If the perimeter is 68 feet, find the length and width of the room
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Answer 1

♣ Qᴜᴇꜱᴛɪᴏɴ :

• The length of a rectangular room is 2 feet less than twice the width. If the perimeter is 68 feet, find the length and width of the room ?

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♣ ᴀɴꜱᴡᴇʀ :

• Width of the rectangular room = 12 feet

• Length of the rectangular room = 22 feet

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♣ ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴꜱ :

Let Width of the rectangular room be x

Then :

Length of the rectangular room = 2x - 2

Perimeter of Rectangle = 2 × (Length + Width)

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Perimeter of Rectangle = 2 × [(x) + (2x - 2)]

68 feet = 2 × [x + 2x - 2]

68 feet = 2 × [3x - 2]

68 feet = 6x - 4

Adding 4 to both sides :

68 feet + 4 = 6x - 4 + 4

72 feet = 6x

Dividing both sides by 6 :

(72 feet)/6 = (6x)/6

12 feet = x

x = 12 feet

Now we can easily findout values of Length and Width from the value of x

We have :

Width of the rectangular room = x

Length of the rectangular room = 2x - 2

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Substituting the values :

Width of the rectangular room = 12 feet

Length of the rectangular room = ((2 × 12)  - 2) feet = 24 - 2 feet = 22 feet

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Answer 2

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Let's assign variable w to width,and create an expression taht uses the variable w for length

• Length : 2w - 2

• Width: w

Perimeter of a rectangle is found by using the formula:

• $\sf{2l+2w=P}$

This holds true because in a rectangle, the sides opposite to each other are larallel and congruent.

This holds true because in a rectangle, the sides opposite to each other are larallel and congruent. We are given the perimeter in this question, 68 feet,so we can substitute yhia number into the formula to find the perimeter of a rectangle.

We can also substitute the expression for length and width into the formula.

• $\sf{2(2w-2)+2(w)=68}$

Distribute 2 inside the parentheses.

• $\sf{4w-4+2w=68}$

Combine like terms on the left side of the equation.

• $\sf{6w-4=68}$

Add 4 to both sides of the equation.

• $\sf{6w=72}$

Divide both sides of the equation by 6.

• $\sf{w=12}$

The width of the rectangular room is 12 feet, Now substitute this value for w into the expression for length in order to find the length of the room.

• $\sf{l=2w-2}$

• $\sf{l=2(12)-2}$

• $\sf{l=24-2}$

• $\sf{l=22}$

So,the length of the rectangular room is 22 feet and width is 12 feet.