Question

originally a rectangle was twice as long as it was wide when 4m were added to its length and 3m subtracted from its width, the resulting rectangle had an area of 600 sq meters. Find the dimensions of the new rectangle.

Answer 1

Original width

=

18

metres

Original length

=

36

mtres

Step-by-step explanation:

The trick with this type of question is to do a quick sketch. That way you can see what is happening and devise a method of solution.

Tony B

Tony B

Known: area is

width

×

length

⇒

600

=

(

w

−

3

)

(

2

w

+

4

)

⇒

600

=

2

w

2

+

4

w

−

6

w

−

12

Subtract 600 from both sides

⇒

2

w

2

−

2

w

−

612

=

0

⇒

(

2

w

−

36

)

(

w

+

17

)

=

0

⇒

w

=

−

17

It is not logical for a length to be negative in this context

so

w

≠

−

17

w

=

18

⇒

L

=

2

×

18

=

36

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Check

(

36

+

4

)

(

18

−

3

)

=

40

×

15

=

600

m

2