2 Answers | Add Yours
The area of a triangle given the length of the three sides as a, b and c is equal to sqrt[s(s - a)(s - b)(s - c)], where s is the semi-perimeter.
Let the similar triangles be PQR and P'Q'R'. As they are similar, the corresponding sides have a common ratio. PQ/P'Q' = QR/Q'R' = RP/R'P' = c . If the length of the sides of P'Q'R' are p, q, r, the length of the sides of PQR is pc, qc, rc
As the triangles are equal in area: sqrt[s(s - p)(s - q)(s - r)] = sqrt[sc(sc - pc)(sc - qc)(sc - rc)]
=> sqrt[s(s - p)(s - q)(s - r)] = c*sqrt[s(s - p)(s - q)(s - r)]
=> c = 1
This gives the length of the corresponding sides of the triangles as the same.
The triangles are proved congruent by the SSS condition.
By measuring the sides.
We’ve answered 318,933 questions. We can answer yours, too.Ask a question