Search: Side of a rectangle is in the ratio 1:1√2 if the length of the larger sides is 12cm then find its area

Length = 12 cm.

Width = 1/1.414 * 12cm = 8.49 cm.

Area = L * W.

To find the area of a rectangle, we need to know the length and width of the rectangle. In this case, we are given that the sides of the rectangle are in the ratio 1:√2, and the length of the larger side is 12 cm.

Let's assume that the shorter side of the rectangle is x cm. Then, according to the given ratio, the longer side would be x√2 cm.

We know that the length of the longer side is 12 cm, so we can set up the following equation:

x√2 = 12

To solve for x, we can divide both sides of the equation by √2:

x = 12 / √2

Rationalizing the denominator (√2) by multiplying both the numerator and denominator by √2, we get:

x = (12 / √2) * (√2 / √2)
x = (12√2) / 2
x = 6√2

So, the shorter side of the rectangle is 6√2 cm, and the longer side is 12 cm.

Now, to find the area of the rectangle, we simply multiply the length and width:

Area = Length * Width
Area = 12 cm * 6√2 cm
Area = 72√2 cm²

Therefore, the area of the rectangle is 72√2 cm².