solving systems by substitution!!!?

Question

the length of the diagonal of a rectangle is root 20cm and its area is 10 cm^2. determine the length and the width of the rectangle.

Answer 1

This is just like the other problem. Follow the steps (from your previous problem) but replace the "old" numbers with the "new" numbers. So all you have to do is put 10 instead of 100, and then do the calculations. Try it. You will learn.

Answer 2

Sorry i do not have the calculator with me now as i am in the airport passing my time with the PDA phone.

Well, you may try the following formula that derive from it.

Let diagonal of a rectangle , H = Root(20)
Area of the rectangular, A = 10

Formula :
Area of Rectangular, A = L x W ; L = Length, W= Width
Diagonal of Rectangular, H^2 = L^2 x W^2 ; Theorem Pythogoras

This is how it works.

Area of Rectangular, A = L x W
L = W/A

Substitude inside, H^2 = L^2 x W^2 , hence you will get
H^2 = (W/A)^2 x W^2. ....... (1)

No, put all the your value for H and A inside equation 1 and you will get the answer for the W. or in short,

W^4 = (H x A)^2 ;
W = Sqrt (H x A) ;
W = Sqrt (H) x Sqrt (A)
W = 20 x Sqrt (10)

Once you get your W, then substitude inside to get your L

Answer 3

diagonal = sqrt (20)
area = 10

lets call the sides a & b

a² + b² = 20 by pythagorean thm

ab = 10 given
thus 2ab = 20

combine equations through addition
a² + 2ab + b² = 40
(a + b)² = 40
a + b = sqrt(40)

now combine through subtraction!
a² - 2ab + b² = 0
(a - b)² = 0
a - b = 0
a = b

thus a = b = sqrt(40) / 2 = sqrt(10)

awesome question

Answer 4

Same process as your previous problem. We showed you how to do it.