Question

are these shapes similar?
(image of two rectangles: left rectangle has vertices n, l, k, j with right angles at n, l, k, j, and sides nl=27 m, lk=27 m, kj=27 m, jn=27 m; right rectangle has vertices t, q, r, s with right angles at t, q, r, s, and sides tq=27 m, qr=31 m, rs=27 m, st=31 m)
options: yes, no

Explanation:

Step1: Recall similarity of rectangles

For two rectangles to be similar, their corresponding sides must be in proportion (same ratio) and all angles are right angles (so angle condition is satisfied).
First rectangle (left): all sides are \(27\) m, so it's a square (a special rectangle) with side length \(27\) m.
Second rectangle (right): sides are \(27\) m and \(31\) m, so it's a rectangle with length \(31\) m and width \(27\) m.

Step2: Check side ratios

Calculate the ratio of corresponding sides. For the first rectangle (square) with side \(27\) and the second rectangle with sides \(27\) and \(31\):
Ratio of width (27) to width (27) is \(\frac{27}{27} = 1\), but ratio of length (27) to length (31) is \(\frac{27}{31}
eq1\). Since not all corresponding sides are in the same ratio, the rectangles are not similar.

Answer:

no