Question

Originally a rectangle was twice as long as it is wide. When 4 m were added to its length
and 3 m subtracted from its width, the resulting rectangle had an area of 600 m2. Find the
dimensions of the new rectangle.​

Answer 1

Answer:

$\huge\underline\bold\red{AnswEr}$

• Original width =18 metres. Original length =36 mtres. Explanation: The trick with this type of question is to do a quick sketch.

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

If the length of a rectangle = x unit

Width of the rectangle = y unit

Then area of the rectangle = xy sq. Unit

CALCULATION

Let width of the rectangle = x metre

Now the rectangle was twice as long as it is wide

So length = 2x cm

So area $= 2x \times x = 2 {x}^{2} \: \: {metre}^{2}$

When 4 metre were added to its length

Then new length = $= (2x + 4) \: \: metre$

When 3 metre is subtracted from its width

New width $= (x - 3) \: \: metre$

By the given condition

$(2x + 4)(x - 3) =6 00$

$\implies \: \: 2 {x}^{2} - 6x + 4x - 12 = 600$

$\implies \: 2 {x}^{2} - 2x - 612 = 0$

$\implies \: {x}^{2} - x - 306 = 0$

$\implies \: {x}^{2} - 18x + 17x- 306 = 0$

$\implies \: {x}(x - 18) + 17 (x- 18) = 0$

$\implies \: (x - 18) (x + 17)= 0$

So

$either \: \: \: (x - 18) = 0 \: \: \: or \: \: (x + 17) = 0$

x - 18 = 0 gives x = 18

Again x + 17 = 0 gives x = - 17

Since width of a rectangle can not be negative

So $x \: \ne \: - 17$

So

$x = 18$

Therefore Length of the rectangle =

$2 \times 18 = 36 \: \: metre$

Width of the rectangle = 18 metre