Image suitcase fitting

Calculate if a rectangular image with dimensions of 33cm and 70cm fits in a suitcase with 65cm, 40cm, and 20cm. Make a sketch, and write it down as a word problem.

Result

q=

Yes

No

Step-by-step explanation:

$$\begin{gathered} a=65\text{cm} \\ b=40\text{cm} \\ c=20\text{cm} \\ x=33\text{cm} \\ y=70\text{cm} \\ s=\sqrt{a^2+b^2+c^2}=\sqrt{65^2+40^2+20^2}=5\sqrt{249}\text{cm}\doteq 78.8987\text{cm} \\ s>y \\ {d}_1=\sqrt{a^2+b^2}=\sqrt{65^2+40^2}=5\sqrt{233}\text{cm}\doteq 76.3217\text{cm} \\ {d}_1>y\wedge x>c \\ {d}_2=\sqrt{a^2+c^2}=\sqrt{65^2+20^2}=5\sqrt{185}\text{cm}\doteq 68.0074\text{cm} \\ {d}_2<y\wedge b>x \\ {d}_3=\sqrt{b^2+c^2}=\sqrt{40^2+20^2}=20\sqrt{5}\text{cm}\doteq 44.7214\text{cm} \\ {d}_2<y\wedge a>x \\ q=0 \end{gathered}$$

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