SOLUTION: find the sides of a rectangle whose perimeter is 40 and diagonal is 18?

Question 375207: find the sides of a rectangle whose perimeter is 40 and diagonal is 18?
Found 2 solutions by unlockmath, mananth:
Answer by unlockmath(1688) (Show Source): You can put this solution on YOUR website!
Hello,
Lets have x be the width and y be the length. We can set up two equations as:
2x+2y=40
x^2+y^2=18^2
With the first equation lets do this:
y=20-x
Now substitute this into the second equation:
x^2+(-x+20)^2=18^2
This can be rewritten as:
x^2+x^2-40x+400=324
Subtract 324 from both sides and combine like terms to get:
2x^2-40x+76=0
Rewritten as:
2(x^2-20x+38)=0
From here you can use the quadratic formula to solve for x and then you can solve for y.
Got it?
RJ
www.math-unlock.com
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
perimeter = 40
2(L+W)=40
L+W=20
L= 20-W
...
Diagonal = 18
..
width^2 + length^2 = diagonal ^2
W^2+(20-W)^2=diagonal^2
W^2+400-40W+W^2=D^2
2W^2-40W+400 = 18^2
2W^2-40W+400=324
2W^2-40w+76=0
/2
W^2-20W+38=0
..
find the roots x1 & x2 by using quadratic formula
discriminant b^2-4ac=248
x1=((20+sqrt(248))/2
x1= 17.87
x2=((20-sqrt(248))/2
2.13
the other side will be 20-17.87 = 2.13
..
m.ananth@hotmail.ca
RELATED QUESTIONS
Find the perimeter of the rectangle whose length is 40cm and a diagonal is... (answered by josgarithmetic)
find the perimeter of the rectangle whose length is 40cm and a diagonal is... (answered by ikleyn)
If the Perimeter of a rectangle is 40 and the diagonal is 12 find the... (answered by Tanzem)
find the perimeter of rectangle whose length is 150m and diagonal is... (answered by josgarithmetic,ikleyn)
What is the area of a rectangle whose perimeter is 92 and the diagonal of... (answered by josgarithmetic,ikleyn)
Find the Perimeter of the Rectangle whose length 40cm and Diagonal is... (answered by josgarithmetic)
The area of a rectangle is 8, and its perimeter is 18. Find its dimensions and diagonal. (answered by ikleyn)
The perimeter of a rectangle is 16, and its diagonal is square root of 40. Find its... (answered by Photonjohn)
find the length and the width of a rectangle whose perimeter is 18 ft whose area is 20... (answered by ankor@dixie-net.com)