the perimeter of rectangle y is equal to its area. rectangle z has the same perimeter as rectangle y. the length of rectangle z is 5 inches and the width is 3 inches. explain how you can find the length and eidth of rectangle y.
perimeter = 2*5+2*3 = 16
2L + 2 W = 16 so L+W=8
WL = 16 so W = 16/L
L + 16/L = 8
L^2 + 16 = 8L
L^2 -8L + 16 = 0
(L-4)(L-4) = 0
L = 4
B = 16/L = 4
from the first description
length ---- x
width ---- y
xy = 2x + 2y
xy - 2y = 2x
y(x-2) = 2x
y = 2x/(x-2)
2nd rectangle is 5 by 3, so its perimeter is 30
so now we know 2x+2y = 30
or x+y = 15
y = 15-x
sub that into the other equation, so
2x/(x-2) = 15-x
2x = 15x - x^2 - 30 + 2x
x^2 -15x + 30 = 0
by the formula
x = 12.623, and subbing back: y = 2.376
or x = 2.376 and subbing back x = 12.623
(notice 2.376 x 12.623 = 29.992 or 30 as expected
I must have have a had a brain-twitch
A 3 by 5 rectangle has a perimeter of 30 ????
Come on Reiny !!!!
i don't get that helppp
No help :(
what is the greatest perimeter of a rectangle wiht an area of 39 square feet
To find the length and width of rectangle Y, we need to use the information given and set up an equation based on its given properties.
Let's suppose the length of rectangle Y is represented by 'L' and its width is represented by 'W'.
Given that the perimeter of rectangle Y is equal to its area, we can set up the equation:
Perimeter of Y = 2(L + W) = Area of Y = L * W
According to the problem, rectangle Z has the same perimeter as rectangle Y. Since the perimeter of rectangle Z is given as 2*(length + width), we can equate the perimeters of Z and Y:
2(5 + 3) = 2(L + W)
Now, we can solve this equation to find the values of L and W.
First, simplify both sides of the equation:
10 + 6 = L + W
Next, combine like terms:
16 = L + W
Since we don't know the exact values of L and W, we cannot find their individual values. However, we can express the length or the width in terms of the other variable.
For example, we can express the length 'L' in terms of 'W':
L = 16 - W
Or we can express the width 'W' in terms of 'L':
W = 16 - L
Therefore, the length and width of rectangle Y cannot be determined based solely on the given information.