A windowpane is 48 inches by 36 inches. What is the distance between opposite corners of the windowpane?

Answer 1

Draw the distance between opposite corners of the windowpane, which is the diagonal line from corner to corner (e.g. from lower left corner to upper right corner). We have now made 2 right triangles. The base and height of the window are the 2 legs of a right triangle and we are being asked to find the hypotenuse. So, we use the Pythagorean Theorem: a² + b² = c². "a" and "b" are the legs of the right triangle while "c" is the hypotenuse. So, 36² + 48² = c². --> 3600 = = c² --> 60 = c.

If doing this without a calculator, it saves time to recognize that 36:48 is a 3:4 ratio, so our triangle is a larger version of a 3,4,5 right triangle. The scale factor (number you multiply the small triangle by to get the big triangle) is 36/3 = 12. So, the hypotenuse of the big triangle must be 12 times as long as the hypotenuse of the small triangle (5). 12(5) = 60.