Evan bought two square rows the larger one measure 12 ft Square the smaller one had an area equal to 1/4 the area of the larger one what fraction of the side length of the larger rug with a side length of the smaller one

The smallest area is:

A2 = (1/4) * (A1)

Substituting:

A2 = (1/4) * (12)

A2 = 3 feet ^ 2

Since both are squares then:

L2 = root (3)

L1 = root (12)

The relationship is:

L2 / L1 = (root (3)) / (root (12))

Rewriting:

L2 / L1 = (root (3)) / (root (3 * 4))

L2 / L1 = (root (3)) / (2raiz (3))

L2 / L1 = 1/2

Answer:

The fraction of the side length of the larger rug with a side length of the smaller one is:

L2 / L1 = 1/2