Window

Peter knocked a 100 × 67 cm opening in the wall for a window frame. When the glazier installs the frame and glass, the glass will be 13.5 cm from the edge of the opening on each side.

By what percentage less light enters through the glass than through the full opening?

Final Answer:

p =  56.4 %

Step-by-step explanation:

$$\begin{gathered} a=100\text{cm} \\ b=67\text{cm} \\ \Delta =13.5\text{cm} \\ {S}_1=a\cdot b=100\cdot 67=6700{\text{cm}}^2 \\ {S}_2=(a-2\cdot \Delta )\cdot (b-2\cdot \Delta )=(100-2\cdot 13.5)\cdot (67-2\cdot 13.5)=2920{\text{cm}}^2 \\ p=100\cdot \frac{S_1-S_2}{S_1}=100\cdot \frac{6700-2920}{6700}=56.4\% \end{gathered}$$

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