+1490 The rectangle with the area of 12 cm2 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 a1 and b1
+129899 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
a1 = b = 4√72
b1 = a/2 = [√2 4√72] / 2
