rA group of architecture students are given the task of designing the layout of a house with a rectangular floorplan. There are no restrictions on the length and the width of the house, but the floor area must be $120$120 square metres. Each student will be allocated a rectangle with a different pair of dimensions to any other student's.

a

Complete the table for the various widths given:

Width in metres ($x$x) |
$5$5 | $10$10 | $15$15 | $20$20 | $25$25 |
---|---|---|---|---|---|

Length in metres ($y$y) |
$\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |

b

Form an equation for $y$`y` in terms of $x$`x`.

c

As the width of the house increases, what happens to the length of the house?

It increases.

A

It decreases.

B

It stays the same.

C

It increases.

A

It decreases.

B

It stays the same.

C

d

If the width is $24$24 metres, what will be the length of the floor area?

e

Graph the relationship relating the width and length of the house.

Loading Graph...

f

Theoretically, how many students could be given unique dimensions, if the dimensions do not have to be whole number values?

$67$67

A

$10$10

B

$100$100

C

An infinite number.

D

$67$67

A

$10$10

B

$100$100

C

An infinite number.

D

Easy

Approx 5 minutes

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