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 (figure shows rectangle abcd with ab = 9 mm and rectangle urst with rs = 15 mm)

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 ABCD and URST

From the figure, in rectangle ABCD, one side (AB) is 9 mm, and in rectangle URST, the corresponding side (RS) is 15 mm? Wait, no, wait. Wait, congruent rectangles: so the length and width of ABCD should match URST. Wait, AB is 9 mm, and RS is 15 mm? Wait, no, maybe AB corresponds to UR or ST, and AD corresponds to RS or UT. Wait, actually, in a rectangle, area is length × width. Since they are congruent, the sides of URST should be equal to ABCD. Wait, looking at the figure, ABCD has AB = 9 mm, and URST has RS = 15 mm? Wait, no, maybe I got the sides wrong. Wait, the problem says rectangle ABCD is congruent to URST. So, the length and width of ABCD are equal to URST. So, if in ABCD, one side is 9 mm (AB) and in URST, one side is 15 mm (RS), but wait, no, maybe AB corresponds to UR, and AD corresponds to RS? Wait, no, maybe the sides are 9 mm and 15 mm? Wait, no, let's think again. The area of a rectangle is length × width. Since they are congruent, the area of URST is equal to area of ABCD. So, if ABCD has sides 9 mm and 15 mm? Wait, AB is 9 mm, and maybe AD is 15 mm? Wait, no, the figure shows ABCD with AB = 9 mm, and URST with RS = 15 mm. Wait, maybe AB (9 mm) corresponds to UR, and AD corresponds to RS (15 mm). So, area of ABCD is 9 mm × 15 mm = 135 mm². Therefore, area of URST is also 135 mm².

Answer:

135 mm² (Option: 135 mm²)