The rectangle with the area of 12 cm^{2}* *has a specific ratio a : b. When folded in half along the longer sides, a new, smaller rectangle, has the same ratio as the original one. Find the sides a and b, and the sides of a new rectangle a_{1} and b_{1}

Dragan Dec 25, 2019

#1**+2 **

Let a be the longer side of the original rectangle and b be the shorter side

So

a*b =12

b = 12/a (1)

When folded in half, the longer side = b and the shorter side is a/2

a/ b = b / (a/2)

a/b = 2b / a

a^2 = 2b^2

a = √2b

So

a * b = 12

√2 b* b = 12

b^2 = 12/√2

b^2 = 6√2

b^2 = √72

b = ^{4}√72

And a = √2 ^{4}√72

So

a / b = √2 ^{4}√72 / [ ^{4}√72 ] = √2

And b/ [a/2] = 2b / a = 2 ^{4}√72 / [√2 ^{4}√72 ] = 2/√2 = √2

So

a = √2 ^{4}√72

b = ^{4}√72

And

a_{1} = b = ^{4}√72

b_{1} = a/2 = [√2 ^{4}√72] / 2

CPhill Dec 25, 2019