We want all angles formed by the shelves and the vertical supports to be right angles. This means that quadrilaterals PMNO and QPOR should be rectangles.
Notice that they are congruent polygons as they have the same corresponding side lengths and angle measures. Recall that in a rectangle diagonals are congruent, so we need to evaluate only one diagonal to determine the appropriate length of the metal support.
As we can see, triangle QRO is a right triangle, which means that we can use the Pythagorean Theorem to find the length of QO. Let's recall this theorem.
a^2+b^2=c^2
In this theorem, a and b are legs of this triangle, and c is the hypotenuse. We can substitute 15 inches and 3 feet for a and b, and solve for c. Remember that we need to convert feet into inches first, so we will multiply 3 by 12 since there are 12 inches in one foot.
