Question

The areas of similar triangles `DeltaABC` and `DeltaDEF` are equal. If the longest side of `DeltaDEF` measures 25 units, what is the length of the longest side of `DeltaABC`?

A.
5 units

B.
25 units

C.
50 units

D.
75 units

Answer 1

There is a theorem which states that "If the areas of two similar triangles are equal then the triangles are congruent."

So, the longest side of Δ DEF will be congruent to ΔABC.

Longest side of Δ DEF ≡ Longest side of ΔABC.

Suppose in the diagram, the longest side of the Δ DEF is EF and longest side of Δ ABC is BC.

So, EF = BC

Since, EF= 25 units is given.

So, BC= 25 units.

Hence, longest side of triangle ABC is 25 units.