Question

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.

Answer 1

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