Question

The areas of two similar triangles are 75m2 and 300m2. The length of one of the sides of the second triangles is 9m. What is the length of the corresponding side in the first triangle?

Answer 1

Answer:

4.5 m

Step-by-step explanation:

The area of two similar triangles are 75 m2 and 300 m2. This gives you the scale factor of the triangles:

$\dfrac{A_{small}}{A_{large}}=k^2\Rightarrow k^2 =\dfrac{75}{300}=\dfrac{3}{12}=\dfrac{1}{4}\Rightarrow k=\dfrac{1}{2}.$

Then you can find the length of the corresponding side:

$\dfrac{side_{small}}{side_{large}}=k\Rightarrow =\dfrac{side_{small}}{9}=\dfrac{1}{2},\ side_{small}=\dfrac{9}{2}=4.5\ m.$