Since the two figures are similar, it can be deduced that the corresponding sides, including the diagonals, will have a common ratio. This ratio is,
d₁ / d₂ = 12 inches / 22 inches
The ratio of their areas should be the square of this ratio.
If we let x be the area of the larger rectangle, we have the equation,
A₁ / A₂ = (d₁/d₂)² = (72 inches² / x inches²)
Substituting the known values,
(12 /22)² = (72 inches² / x inches²)
The value of x is equal to 242 inches². Thus, the area of the larger rectangle is 242 inches².
