Question

An artist is going to cut four similar righttriangles from a rectangular piece of paperlike the one shown to the right. What is thedistance from B and D to the diagonal AC?Write an equation and solve, showing ALLthe work.

Answer 1

First let's find the length of AC using the Pythagorean theorem in the right triangle with legs of 5 and 12:

`\begin{gathered} AC^2=5^2+12^2 \\ AC^2=25+144 \\ AC^2=169 \\ AC=13 \end{gathered}`

So the diagonal of the rectangle is 13 units. Now, since the area of a triangle is calculated as the product of a base and the corresponding height, we can use the legs as base and height or we can use the segment AC and the corresponding height, and the result is the same, so we have:

`\begin{gathered} A=(b\cdot h)/(2) \\ A=(5\cdot12)/(2) \\ A=(13\cdot h)/(2) \\ \\ (5\cdot12)/(2)=(13\cdot h)/(2) \\ 60=13h \\ h=(60)/(13) \end{gathered}`

So the distance from B or D to the diagonal AC is 60/13 units.