Question

triangles ABC and DEF are similar. The lengths of the sides of ABC are 140,120, and 110. The length of the smallest side of DEF is 260, what is the length of the longest side of DEF?

Answer 1

The longest side is 330.9 units.

Explanation:

Since the triangles are similar, the ratio of the corresponding sides of two triangles is equal.

In other words,

`(AB)/(DE) = (BC)/(EF) = (CA)/(FD)`

The lengths of the sides of triangle ABC are

AB = 140 , BC = 120 , CA = 110

The length of smallest side of triangle DEF is 260.

Thus,
`(CA)/(FD) = (110)/(260) = (11)/(26)`

thus,

`(AB)/(DE) = (11)/(26) = (140)/(DE)`

So, DE = 330.9 units

similarly,

`(BC)/(EF) = (11)/(26) = (120)/(EF)`

So, EF = 283.636 units

Thus the sides of triangle are 260, 283.636 and 330.9 units.

The longest side is 330.9 units.