Question

rectangle abcd is congruent to rectangle urst. what is the area of rectangle urst?
image of two rectangles: abcd with segment ab labeled 9 mm, urst with segment rs labeled 15 mm. options: 24 mm, 48 mm, 135 mm², 144 mm². figure may not be drawn to scale.

Explanation:

Step1: Recall congruent rectangles property

Congruent rectangles have equal corresponding sides and equal areas. So, the area of rectangle \( URST \) is equal to the area of rectangle \( ABCD \).

Step2: Identify sides of rectangle \( ABCD \)

From the figure, one side of rectangle \( ABCD \) is \( AB = 9\space mm \), and the corresponding side of rectangle \( URST \) (since they are congruent) will have the other side as \( RS = 15\space mm \) (corresponding side to the other side of \( ABCD \)).

Step3: Calculate area of rectangle

The area of a rectangle is given by the formula \( A = \text{length} \times \text{width} \). For rectangle \( URST \) (same as \( ABCD \) in area), length \( l = 15\space mm \) and width \( w = 9\space mm \). So, area \( A=15\times9 \).
\( 15\times9 = 135\space mm^2 \)

Answer:

\( 135\space mm^2 \) (corresponding to the option "135 \( \text{mm}^2 \)")