A rectangles length and width are a ratio of 8:5. The area is 169 square millimeters. What are the length and width?
Can anyone help and show how they got the answer....lost on this one.
width --- 5x
length ---8x
(5x)(8x) = 169
40x^2 = 169
x^2 = 169/40
x = 13/√40
width is 65/√40 = appr 10.28
length is 104√40 = appr 16.44
check:
area = (65/√40)(104/√40) = 6760/40 = 169
ratio = (65/√40) : 104/√40)
= 65 : 104
= 5 : 8
the dimensions are 8x and 5x. So,
8x * 5x = 169
40x^2 = 169
x^2 = 169/40
x = 13/√40
Now you can determine 8x and 5x
To solve this problem, we need to understand the relationship between the ratio, area, length, and width of a rectangle.
Let's assume that the length and width of the rectangle are 8x and 5x, respectively, where x is a constant. This is based on the given ratio of 8:5.
The formula for the area of a rectangle is length multiplied by width, so we can write this as:
Area = length * width
Substituting the values, we have:
169 = (8x) * (5x)
Now, we can solve this equation to find the value of x.
169 = 40x^2
Dividing both sides of the equation by 40 gives:
4.225 = x^2
Taking the square root of both sides, we get:
x ≈ ±2.057
Since length and width cannot be negative, we take the positive value:
x = 2.057
Now, we can find the length and width by substituting this value back into the expressions:
Length = 8x ≈ 8 * 2.057 ≈ 16.456 millimeters
Width = 5x ≈ 5 * 2.057 ≈ 10.285 millimeters
Therefore, the length of the rectangle is approximately 16.456 millimeters, and the width is approximately 10.285 millimeters.