The ratio of the perimeters of two similar triangles is 4:3. What are the areas of these triangles if the sum of their areas is 130cm^2?

Question

anonymous · Answer

@Zarkon

anonymous · Answer

@Hero

anonymous · Answer

for similar triangles the ratio of the areas is equal to ratio of the squares of their sides

anonymous · Answer

here the ratio of the sides is 4:3  ( ratio of corresponding sides = ratio of perimeters)
thus their areas is in the ratio of areas is 16:9

anonymous · Answer

thus area of one of the triangle =16/(16+9)  * 130 =83.2
and that for the other triangle is 9/(16+9)  *130  =46.8

whpalmer4 · Answer

If you're wondering why the ratio of the areas is the ratio of the squares of the sides, consider that the area is $\dfrac{1}{2}bh$, and so we will be multiplying both $b$ and $h$ by the scale factor.