serious math problem help please?

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...

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!

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!

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

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

There are many ways to solve this problem.

You know the width of the path is 2m. If it were all in a straight line, then the length of the path L multiplied by the width 2m, will give you the outer area 136m2.

You could divide the area of the path into 4 equal parts that will surround the center lawn area. Just divide L by 4 to get the length of one piece.

So one quarter of the outer area is 136m2/4=34m2

Because area is length * width, and you know the width is 2m, L * 2m = 34m2 so L =17m

If you divide your perimeter into 4 sections, like boards of equal length set into a square, where the first 2 meters of one outer edge is the width of the previous board, and the rest is the next board. You will see that the first width is 2m, followed by 17m you just calculated (19m total outer length of one side). So the inner length of the square, is 19m -2m -2m =15m.

If the inner area is square and has a length of 15m on a side, the area is 15m*15m = 225m2

Area of Pavement = 4 (2²) + 4 (2X)

where:

X = side of the lawn

136 m² = 16 + 8X

X = 120 / 8

X = 15 m

Area of Lawn = X²

= 225 m²

Let x be the width of the lawn and path.

x²=the area of the lawn and path

(x-2)²=x²-4x+4 = area of lawn without path

x²-(x²-4x+4) = area of path = 136m²

= x²-x²+4x-4 = 4x-4

4x-4=136

4x=140

x=35

so, the area of the lawn = (x-2)² = (35 - 2)² = 33² = 1089

if the path area is 136 sq m and it is 2 m wide---then it is 68 m long. 68/4 (since the garden is square) = 17 m in each direction. Since the path is 2 m larger than each side in each direction the length of each side of the garden is 17-4 or 13 m. Area of the garden =lXw or 13x13 which is 169 sq m.

let the length of one side of the lawn be=l .

its area=l^2.

area of the path=(l+2)^2-l^2=136

4l=132

l=33m

desired area=33^2=1089m^2