Question

Two triangles are proportional, and the first triangle has a base of 10 cm and a height of 8 cm. If the base of the second triangle is 15 cm, what is the height of the second triangle?

Answer 1

If two triangles, A and B, are proportional, this means that exists some number k such that:

`\begin{gathered} Base_B=Base_A\cdot k \\ Height_B=Height_A\cdot k \end{gathered}`

We know that:

Triangle A:

BaseA = 10cm

HeightA = 8cm

Triangle B:

BaseB = 15cm

HeightB = x

Then, we can find k by:

`15=10\cdot k`

And solve:

`k=(15)/(10)=1.5`

Now that we know the value of k, we can find the unknown height:

`Height_B=8\cdot1.5=12`

Thus, the answer is:

The height of the second triangle is 12cm