What are the width and the length of a 1m2 rectangle, if the relation L/W is the square root of 2?

Question

1m2 (one square meter = 10,000 cm2)

Answer 1

A = L*W = 1m^2

L / W = sqrt (2)
gives, L = W sqrt(2)

substitution into area:
1m^2 = [W sqrt(2)](W)
1m^2 = W^2 sqrt(2)
W^2 = 1m^2 / sqrt(2)
W = sqrt [1m^2 / sqrt(2)]
W ~= 0.84m

L = W sqrt(2)
L = (0.84m) * sqrt(2)
L ~= 1.19m

Answer 2

If that first response is all you need, solve it yourself and give the "Best answer" there.

But if you need a bit more, scroll down.











Square root is power 1/2, sqrt(2) = 2^(1/2)

Substituting as the first answer says,

W^2 = 1/(2^(1/2))

Take the square root of both sides means raise both sides to the power 1/2

W = 1/(2^(1/4)) since multiplying the indices gives
(1/2)*(1/2) = 1/4

Then L = [2^(1/2)]/[2^(1/4)]
= 2^(1/4) since subtracting indices gives
1/2 - 1/4 = 1/4

Answer 3

Since L/W = root 2, L=Wroot2. Plop Wroot2 in for L in the area formula for the rectangle. Now you have an equation in one variable (W) that you can solve without too much fuss.

Answer 4

let x n y are l n b
x/y=2^(1/2)
x=y2^(1/2)

xy=1
y2^(1/2)y=1
y^2=1/(2^(1/2))
y=2^(-1/4)

u can evaluate x also