### Brain Teasers

# Equal Mowing

Mad Ade's kids, Mad Ade junior and little Miss Mad Ade were going to cut the grass on their square lawn, while their dad was out buying a bumper family sized kebab with extra grease. They agreed that each should cut one-half of the area. Junior went first, and cut a border 2 metres wide all the way around.

After doing a few sums, Little Miss agreed that exactly one-half had been cut and happily cut the rest.

What was the area of the lawn?

After doing a few sums, Little Miss agreed that exactly one-half had been cut and happily cut the rest.

What was the area of the lawn?

### Answer

Area of lawn was 186.51 square metresHide Answer Show Answer

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## Comments

lol the "bumper family sized Kebab with extra grease" is so random

hmmm. a random occurrence that keeps occurring. in bizarro-world the answer could also be 5.49

how did you get the answer though mad?

I don't understand how you come up with the answer. Why do you sometimes fail to give an explanation? Is it because you think you're better than us and don't have to explain?

imagine a square with a 2 meter border around the sides.

one side of the square would be 2 meters + x meters + 2 meters wide = (x + 4) meters.

one side of the inner square that will be formed (minus the border) will be x meters.

2x^2 = (x + 4)^2

2x^2 = x^2 + 8X + 16

x^2 - 8X - 16 = 0

use quadratic formula for solving an equation in the form: ax^2 + bx + c = 0

x = (-b +/- sqrt(b^2 - 4ac)) / 2a

you'll arrived at the answers

x = 9.656854249,

x = -1.656854249.

area of the bigger square(including border):

area = (x + 4)^2

= (9.656854249 + 4)^2

= 186.509668

or as emmm said:

area = (x + 4)^2

= ((-1.656854249) + 4)^2

= 5.490332008

one side of the square would be 2 meters + x meters + 2 meters wide = (x + 4) meters.

one side of the inner square that will be formed (minus the border) will be x meters.

2x^2 = (x + 4)^2

2x^2 = x^2 + 8X + 16

x^2 - 8X - 16 = 0

use quadratic formula for solving an equation in the form: ax^2 + bx + c = 0

x = (-b +/- sqrt(b^2 - 4ac)) / 2a

you'll arrived at the answers

x = 9.656854249,

x = -1.656854249.

area of the bigger square(including border):

area = (x + 4)^2

= (9.656854249 + 4)^2

= 186.509668

or as emmm said:

area = (x + 4)^2

= ((-1.656854249) + 4)^2

= 5.490332008

Actually you can't have an area of 5.49.

As pating posted above, the sides of the inner square would be 9.66 or -1.66. Since you can't have a negative length, the only acceptable answer would be 186.51.

As pating posted above, the sides of the inner square would be 9.66 or -1.66. Since you can't have a negative length, the only acceptable answer would be 186.51.

Sorry Jota. You can have an area of 5.49. We won't disturb Pythagoras's grave just yet.

x^2 = 2(x-4)^2 since area is double inside square.

x^2 = 2x^2 - 16x + 32

x^2 - 16x + 32 = 0

(x - ^2 = 32

x - 8 = root(32) = 4root(2)

x = 8 + 4root(2)

Area = (8+4root(2))^2 = 96+64root(2) exactly!

x^2 = 2(x-4)^2 since area is double inside square.

x^2 = 2x^2 - 16x + 32

x^2 - 16x + 32 = 0

(x - ^2 = 32

x - 8 = root(32) = 4root(2)

x = 8 + 4root(2)

Area = (8+4root(2))^2 = 96+64root(2) exactly!

I enjoyed doing this but I don't think that text book maths questions make good Brain Teasers unless there is something particularly clever about them. Having to use the quadratic formula is a bit specialised (in my humble opinion!)

I still enjoyed it, though ... and agree with the one solution offered.

I still enjoyed it, though ... and agree with the one solution offered.

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