Question

Let A be the area of a triangle with sides of length 25,25 and 30.Let B be the area of a triangle with sides of length 25,25, and 40.Find A/BDraw diagrams to represent the two triangles and label them with their dimensions. Use the formula for the area of a triangle to find A and B.

Answer 1

We have 2 triangles:

Let H be the height of the second triangle and h the height of the first triangle. Hence, their area are given by

`\begin{gathered} A=(25\cdot h)/(2) \\ B=(25\cdot H)/(2) \end{gathered}`

From these relations, we have

`(A)/(B)=((25\cdot h)/(2))/((25\cdot H)/(2))`

By using the sandwich law, this is equal to

`(A)/(B)=(2(25\cdot h))/(2(25\cdot H))`

Finally, the answer is

`(A)/(B)=(h)/(H)`