Question

rectangle abcd is congruent to rectangle urst. what is the area of rectangle urst? 24 mm 48 mm 135 mm² 144 mm² figure may not be drawn to scale.

Explanation:

Step1: Recall the property of congruent rectangles

Congruent rectangles have equal areas.

Step2: Use the formula for the area of a rectangle

The formula for the area of a rectangle is \(A = l\times w\). For rectangle \(ABCD\), if we assume \(AB = 9\space mm\) (width) and for rectangle \(URST\), \(RS=15\space mm\) (length). Since \(ABCD\cong URST\), the area of \(URST\) is same as the area of \(ABCD\). But wait, no—actually, for a rectangle, area \(A = \text{length}\times\text{width}\). If we consider that in congruent rectangles, corresponding sides are equal. Let's assume that the sides of the rectangles: if \(AB = 9\space mm\) and \(RS = 15\space mm\) (but no, wait, actually, the formula for area of rectangle \(A=\text{length}\times\text{width}\). Since \(ABCD\cong URST\), their areas are equal. If we assume that one side is \(9\space mm\) and the other is \(15\space mm\) (because in a rectangle, opposite sides are equal and for congruent rectangles, all corresponding sides are equal). So \(A = 9\times15\)
$$A=9\times15 = 135\space mm^{2}$$

Answer:

\(135\space mm^{2}\) (the third option)