Right-angled 66364

From a rectangular board with dimensions of 2 m and 3 m, we cut isosceles right-angled triangles at the corners with an overhang of 40 cm. Calculate the ratio of the areas of the rest of the board to its total original area.

Correct answer:

x =  71:75

Step-by-step explanation:

$$\begin{gathered} a=2\text{m} \\ b=3\text{m} \\ t=40\text{cm}\to \text{m}=40:100\text{m}=0.4\text{m} \\ {S}_1=a\cdot b=2\cdot 3=6{\text{m}}^2 \\ {S}_2=4\cdot \frac{t\cdot t}{2}=4\cdot \frac{\frac{2}{5}\cdot \frac{2}{5}}{2}=\frac{8}{25}=0.32{\text{m}}^2 \\ {S}_3=S_1-S_2=6-\frac{8}{25}=\frac{6\cdot 25}{25}-\frac{8}{25}=\frac{150}{25}-\frac{8}{25}=\frac{150-8}{25}=\frac{142}{25}=5.68{\text{m}}^2 \\ x=\frac{S_3}{S_1}=\frac{\frac{142}{25}}{6}=\frac{71}{75}\approx 0.9467=71:75 \end{gathered}$$

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