serious math problem help please?

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Since we know there's a 2m path surrounding it and the path area is 136m^2, we know...

let x=side of square lawn

(x+2)(x+2)-(x)(x)=136
x^2+4x+4-x^2=136 x^2 cancels
4x+4=136
4x=132
x=33

Since x is one side of the square lawn, x^2=1089, which is the total area of the square lawn.

Now check.
(x+2)(x+2)-(x)(x)
35^2-33^2=136m^2 <- Same as information given.

There. All other answers will be similar or elaborations.

You can also go into dimensions...but I don't think you've learned it yet, and there's no point introducing this concept if you're not doing physics. It'll just be confusing......Show more

There are a lot of incorrect answers here, especially the first one.

Draw a picture. if you divide 136 m² by 4, you will get the area of one side of the path, plus two triangles on the end. These two triangles can be stuck together to form a square with an area of (2 m)², or 4 m². So, the area of the path next to one side of the lawn is ( 136 / 4 ) – 4 = 30 m². This is a rectangle.

Now, we know how wide the path is, so we can divide 30m² by 2 m to get 15 m.

There is an important difference here. First, we were dividing by a "dimensionless" number, which is a number without a unit. For example, 10 m² divided by 2 is 5 m². The unit doesn't change. But this time, we are dividing by a number with a unit. For example, 10 m² divided by 2 m is 5 m. This is how we can break down a rectangle to figure out its side lengths.

Anyway, we now know the side length of the lawn. It is 30 m² / 2 m = 15 m. Now, since the lawn is a square, we can find the area like this. (15 m)(15 m) = 15² m² = 225 m². Notice how this time the unit changed too.

One way to check if you've done a problem correctly is to make sure that you have used all of the information you have been given. If you answer the problem, but you can't find that you've used how wide the path is, then the answer must be wrong. This is because you can use logic to deduce that the answer would be different if the path was wider in the first place.

Good luck!...Show more

Let the side of the lawn=x meters
Then the area of the lawn is x^2 meters.
The dimension of the square's side that comprises the
path AND the lawn is x+4 meters.
The area of the path and lawn together is thus (x+4)^2
Area of path and lawn - area of lawn= area of path
(x+4)^2 - x^2 = 136
x^2+8x+16-x^2=136
8x+16=136
8x=120
x=15
That's the length of the side of the lawn.
Therefore the lawn's area=15^2, =225 sq. meters.

Check:
Upper and lower areas of path are 2 X (15+4) each
For both upper and lower, area is 2{2 X 19}=76
Left and right areas of path are 15 X 2 each.
For both sides, area is 2{15 X 2}, =60
Total area=76+60, =136 sq. meters

Our answer checks out, and so 225 is correct.
Season's Greetings to you!...Show more

Let L=size of the lawn, so area of lawn = L*L

a 2-m wide path around it would have area
4 x 2(L+2) = 8(L + 2) = 136
L + 2 = 136/8 = 17
L =15
so it's a 15 by 15 m = 225m^2 lawn...Show more

Let width of the square be x
area of the square lawn= x^2

width of the path = 2m
area of the path = 136m ^2

Total Area = (x+4)^ 2 [ including width of the path on both sides]

Area of the path = Total area - Area of the lawn
136 = (x+4)^ 2 - x^2
8x + 16 = 136
x= 15

Therefore, Area of the lawn = 15 *15 =225 m^2...Show more