Question

Find the area. ABCD∼EFGHABCD∼EFGH The area of rectangle ABCD is 72 inches2 and a diagonal is 12 inches. The diagonal of rectangle EFGH is 22 inches. Find the area of rectangle EFGH. Round to the nearest inch2 if necessary.

Answer 1

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.