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The diagram shows a square, of side length x. Inside the square is a shaded triangle with a vertex at a perpendicular distance y from the top edge. If y=1/4x, calculate the fraction of the square that is shaded. Please ignore the pen and scribbles on the diagram.

The Diagram Shows A Square Of Side Length X Inside The Square Is A Shaded Triangle With A Vertex At A Perpendicular Distance Y From The Top Edge If Y14x Calcula class=

Sagot :

[tex]The\ area\ of\ the\ square:A_{\fbox{}}=x^2\\\\The\ area\ of\ the\ triangle:A_\Delta=\frac{1}{2}\cdot\frac{3}{4}x\cdot x=\frac{3}{8}x^2\\\\The\ area\ of\ the\ shaded\ place:\\\\A=A_{\fbox{}}-A_\Delta=x^2-\frac{3}{8}x^2=\frac{8}{8}x^2-\frac{3}{8}x^2=\frac{8-3}{8}x^2=\frac{5}{8}x^2\\\\The\ fraction\ of\ the\ square\ that\ is\ shaded:\frac{A}{A_{\fbox{}}}=\frac{\frac{5}{8}x^2}{x^2}=\boxed{\boxed{\frac{5}{8}}}[/tex]
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