A rectangles length and width are in a ratio of 17:2. The area is 136 square yards. What are the length and width.
Have no idea how to even start to work this problem other than 17L X 2w= 136
It's not 17 by 2. So let's try 34 by 4.
let the sides by 17x by 2x
( ---> ratio is 17x : 2x = 17 : 2 )
34x^2 = 136
x^2 = 136/34 = 4
x = 2
sides are 17(2) by 2(2)
or 34 by 4
To solve this problem, first, let's assign variables to the length and width of the rectangle.
Let L represent the length of the rectangle, and let W represent the width of the rectangle.
We're given that the ratio of the length to the width is 17:2. This can be written as L/W = 17/2.
Since the area of a rectangle is given by A = L * W, we can also set up an equation for the area.
A = L * W = 136 square yards.
From the equation L/W = 17/2, we can rearrange it to solve for one of the variables in terms of the other. Let's solve for L in terms of W.
L/W = 17/2
L = (17/2) * W
Now substitute this expression for L into the equation for the area.
A = L * W = (17/2) * W * W = 136
Simplify the equation.
17 * W^2 / 2 = 136
Multiply both sides of the equation by 2 to eliminate the fraction.
17 * W^2 = 272
Divide both sides of the equation by 17.
W^2 = 16
Take the square root of both sides to solve for W.
W = √16
W = 4
Now substitute this value for W into the equation for L.
L = (17/2) * W = (17/2) * 4 = 34
Therefore, the length of the rectangle is 34 yards, and the width is 4 yards.
To solve this problem, you can set up a proportion using the ratio of the length and width.
Let's assume the length of the rectangle is 17x and the width is 2x, where x is a common factor.
The area of a rectangle is given by the formula: Area = length * width
In this case, the area is given as 136 square yards:
17x * 2x = 136
Now, we can solve for x by dividing both sides of the equation by 34:
(17x * 2x) / 34 = 136 / 34
2x^2 = 4
Next, divide both sides of the equation by 2 to isolate x^2:
x^2 = 2
Take the square root of both sides to solve for x:
√(x^2) = √2
x = √2
Now that we have the value of x, we can find the length and width of the rectangle.
Length = 17x = 17 * √2
Width = 2x = 2 * √2
Therefore, the length is approximately 24.04 yards and the width is approximately 3.20 yards.