Question

c. When measuring the dimensions of a room a carpenter uses a tape measure that only displays a number of feet, L, on the metal tape.
(The carpenter's tape measure does not display inches).
i. Write an expression to determine the length of the room in yards.
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ii. Write an expression to determine the length of the room in units of 3 feet (yards).
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iii. Write an expression to determine how many times as long the room is than 3 feet.
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Answer 1

The dimension of a room is the length and width of the room.

• The length of the room in yard is L/3
• An expression for the length of the room in unit of 3ft is 3L
• The room is longer than 3 feet, in L times

From the question, we have:

$L \to$ Number of feet

(a) An expression for the length of the room in yards

In standard unit of conversion

$1ft = \frac{1}{3} yd$

Multiply both sides by L:

$L \times 1ft = L \times \frac{1}{3} yd$

$L\ ft = \frac{L}{3} yd$

Hence, the length of the room in yard is L/3

(b) An expression for the length of the room in unit of 3ft

In (a), we have:

$L \to$ Number of feet

To calculate the length in units of 3 feet, we simply multiply L by 3

$Unit = 3 \times L$

$Unit = 3L$

An expression for the length of the room in unit of 3ft is 3L

(c) How many times longer the room is, than 3ft.

In (b), we have:

$Unit = 3L$

The number of times (n) the room is longer than 3 ft is:

$n = Unit \div 3$

$n = 3L \div 3$

$n = L$

The room is longer than 3 feet, in L times

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