Question

the diagonal lengths of three rectangles are shown below. the rectangles are not drawn to scale. arrange the rectangles in order by their diagonal lengths from shortest to longest? rectangle p: 6.7 cm; rectangle s: 5\frac{3}{4} cm; rectangle t: sqrt{36.5} cm

Explanation:

Step1: Convert fraction to decimal

$5\frac{3}{4}=5 + \frac{3}{4}=5 + 0.75 = 5.75$

Step2: Compare the values

We have the diagonal lengths: $5.75$ cm (Rectangle S), $6.7$ cm (Rectangle P), $\sqrt{36.5}\approx6.04$ cm (Rectangle T)

Since $5.75<6.04 < 6.7$

Answer:

Rectangle S, Rectangle T, Rectangle P