Question

Explain why the triangles are similar.​

Answer 1

The triangles are similar, because the ratio of its corresponding sides is equal

Explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is equal

so

Find the value of x

`(30)/(6.3x+6)=(20)/(25) \\ \\30*25=20*(6.3x+6)\\ \\ 37.5=6.3x+6\\ \\6.3x=37.5-6\\ \\x=31.5/6.3\\ \\x=5\ units`

The value of the hypotenuse in the second triangle is

`(6.3x+6)=6.3*5+6=37.5\ units`

Applying the Pythagoras Theorem find the value of the second leg in both triangles

First triangle

`h1^(2)=30^(2)-20^(2)\\ \\h1^(2) =500\\ \\h1=10√(5)\ units`

Second triangle

`h2^(2)=37.5^(2)-25^(2)\\ \\h2^(2) =(3,125)/(4)\\ \\h2=(25√(5))/(2)}\ units`

Verify the ratios of the corresponding sides

`(20)/(25)=(30)/(37.5)=(10√(5))/((25√(5))/(2))`

`0.8=0.8=0.8` -----> is true

therefore

The triangles are similar