Question

are these shapes similar?
j 40 in k
25 in 25 in
m 40 in l
t
23 in
u 40 in r
23 in
(yes and no buttons)

Explanation:

Step1: Recall similarity of rectangles

For rectangles to be similar, the ratios of corresponding sides must be equal. Let's denote the first rectangle (JKLM) with length \( l_1 = 40 \) in and width \( w_1 = 25 \) in. The second rectangle (STUR) with length \( l_2 = 40 \) in and width \( w_2 = 23 \) in.

Step2: Calculate the ratios of sides

Calculate the ratio of length to width for the first rectangle: \( \frac{l_1}{w_1}=\frac{40}{25}=\frac{8}{5} = 1.6 \)

Calculate the ratio of length to width for the second rectangle: \( \frac{l_2}{w_2}=\frac{40}{23}\approx1.739 \)

Since \( \frac{40}{25}
eq\frac{40}{23} \) (and also \( \frac{25}{40}
eq\frac{23}{40} \) when checking width to length), the corresponding sides are not in proportion.

Answer:

no