The length of Laurie's rectangular swimming pool is triple its width. The pool cover an area of 192 m2. If Laurie swims across the diagonal and back, how far does she travel?
L=Lenght W=Width A=Area D=Diagonal
L=3*W , A=L*W= 3*W*W= 3*W^2=192=3*W^2 3*W^2= 192 W^2=(192/3)=64
W=sqroot(64)= 8 W=8
L=3*W=3*8= 24 L=24
D=sqroot(L^2 + W^2)
D=sqroot(24^2 + 8^2)=sqroot(676+ 64)
=sqroot(640)=sqroot(64*10)
sqroot(64)=8
D=8*sqroot(10)
One correction. My answer is correct, but I make one typefeler.
24^2=576 not 676
D=sqroot(24^2 + 8^2)=sqroot(576+ 64)
=sqroot(640)=sqroot(64*10)
sqroot(64)=8
D=8*sqroot(10)
To find the length and width of Laurie's swimming pool, we can set up a system of equations based on the given information.
Let's assume the width of the pool is x meters.
According to the problem, the length of the pool is triple the width, so it would be 3x meters.
Now, we know that the area of a rectangle is given by the formula: area = length × width.
So, we can write the equation: (3x)(x) = 192
Simplifying this equation, we have:
3x^2 = 192
Now, let's solve for x:
Divide both sides of the equation by 3: x^2 = 64
Take the square root of both sides: x = √64
Simplifying the square root, we have: x = 8
Therefore, the width of Laurie's swimming pool is 8 meters, and the length is 3 times that, which is 24 meters.
To find the diagonal distance across the pool, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides.
Consider the rectangle with length 24 meters and width 8 meters. The diagonal forms the hypotenuse of a right-angled triangle.
Using the Pythagorean theorem, we have:
diagonal^2 = length^2 + width^2
diagonal^2 = (24)^2 + (8)^2
diagonal^2 = 576 + 64
diagonal^2 = 640
To find the diagonal distance, we take the square root of both sides:
diagonal = √640
Simplifying the square root, we have:
diagonal ≈ 25.3 meters
Since Laurie swims across the diagonal and then back, she covers a distance of 2 times the diagonal length.
So, Laurie travels approximately 2 × 25.3 = 50.6 meters.
To find how far Laurie travels when swimming across the diagonal and back, we first need to find the length and width of the rectangular swimming pool.
Let's assume that the width of the pool is "x" meters.
Since the length of the pool is triple its width, the length would be 3 times the width, or 3x meters.
To find the area of the pool, we multiply the length by the width:
Area = Length × Width
192 = (3x) × (x)
192 = 3x^2
To solve this equation, we divide both sides by 3:
192/3 = x^2
64 = x^2
Taking the square root of both sides, we find that:
x = √64
x = 8
So, the width of the pool is 8 meters, and the length is 3 times the width, which is 24 meters.
Now, to find the diagonal, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the diagonal) is equal to the sum of the squares of the other two sides.
Let's assume the diagonal is "d" meters.
According to the Pythagorean theorem:
d^2 = width^2 + length^2
d^2 = 8^2 + 24^2
d^2 = 64 + 576
d^2 = 640
Taking the square root of both sides, we find that:
d = √640
d ≈ 25.3 (rounded to one decimal place)
To find the total distance Laurie travels, we multiply the diagonal by 2:
Total distance = diagonal + diagonal = 25.3 + 25.3
Total distance ≈ 50.6 meters
So, Laurie would travel approximately 50.6 meters when swimming across the diagonal and back.