A rectangular 5

A rectangular picture frame is made of wooden strips ¾ inch wide. The outside edge of the frame is 8 ¼ inches long and 6 ¾ inches wide. Can a rectangular picture 7 inches long and 5 ½ inches wide fit inside the frame? CLEARLY EXPLAIN your answer.

Result

a=

Yes

No

Step-by-step explanation:

$$\begin{gathered} s=3/4=\frac{3}{4}=0.75\text{in} \\ l=8\frac{1}{4}=8+\frac{1}{4}=\frac{8\cdot 4+1}{4}=\frac{32+1}{4}=\frac{33}{4}=8\frac{1}{4}=8.25\text{in} \\ w=6\frac{3}{4}=6+\frac{3}{4}=\frac{6\cdot 4+3}{4}=\frac{24+3}{4}=\frac{27}{4}=6\frac{3}{4}=6.75\text{in} \\ x=7\text{in} \\ y=5\frac{1}{2}=5+\frac{1}{2}=\frac{5\cdot 2+1}{2}=\frac{10+1}{2}=\frac{11}{2}=5\frac{1}{2}=5.5\text{in} \\ X=l-2\cdot s=\frac{33}{4}-2\cdot \frac{3}{4}=\frac{27}{4}=6\frac{3}{4}=6.75\text{in} \\ Y=w-2\cdot s=\frac{27}{4}-2\cdot \frac{3}{4}=\frac{21}{4}=5\frac{1}{4}=5.25\text{in} \\ a=(x<X\wedge y<Y) \\ x>X \\ y>Y \\ a=0 \end{gathered}$$

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