Question

A plot of land doubles in size by adding X meters to the length and X meters to the width of the land. If the original plot had an area of 200 x 300 m, what is the value of X?

Answer 1

Answer:

x=100

Step-by-step explanation:

Original plot

A = 200*300

A = 60000

New plot

The new length is 200+x and the new width is 300+x

A = (200+x) (300+x)

It doubles the area = 60000*2 = 120000

120000 = (200+x) (300+x)

We need to find x

FOIL

120000 = 60000 +300x+200x +x^2

120000 = 60000 +500x +x^2

Subtract 120000 from each side

120000-120000 = 60000-120000 +500x +x^2

0 = x^2 +500x - 60000

Factor

0= (x-100) (x+600)

Using the zero product property

x=100 or x=-600

Since we cannot add negative land

x=100

Answer 2

The area of the original plot is

200 ×300 =60000

The problem

$(x + 200)(x + 300) = 120000 \\ proof.300 \times 400 = 120000 \\ x {}^{2} + 500x + 60000 = 120000 \\ x {}^{2} + 500x - 60000 = 0 \\ (x + 600(x - 100) = 0 \\so.... \\ x = - 600(reject) \: x = 100 \\ x = 100meter \\ proof.300 \times 400 = 120000$

Hope this help :)