Question

The smaller of two similar triangles has a perimeter of 20cm (`a+b+c=`20cm). The lengths of the longest sides of both triangles are in proportion 2:5. What is the perimeter of the larger triangle? Please explain.

Answer 1

`color(white)(xx)50`

Explanation:

`color(white)(xx)a+b+c=20`

Let sides of larger triangle are `a'`, `b'`, and `c'`. If similarity proportion is `2/5`, then,
`color(white)(xx)a'=5/2a`,
`color(white)(xx)b'=5/2b`,
and`color(white)(x)c'=5/2c`

`=>a'+b'+c'=5/2(a+b+c)`
`=>a'+b'+c'=5/2color(red)(*20)`
`color(white)(xxxxxxxxxxx)=50`