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'?

Answer 1

we know that

the ratio of the areas of similar triangles is equal to the squared scale factor

so

Area triangle ABC/Area triangle DEF=(scale factor)²

if area triangle ABC=area triangle DEF

then

(scale factor)²=1---------> scale factor=1

so

the length of the longest side of triangle ABC is equal to the the length of the longest side of triangle DEF

therefore

the answer is

the length of the longest side of triangle ABC is equal to 25 units