The area of similar triangles PQR and MNT are 196 cm2 and 169 cm2 respectively. If the longest side of the larger ∆PQR be 28 cm then what is the length (in cm) of the longest side of the smaller ∆MNT?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 26
Concept used:
Two triangles are similar if their corresponding angles are equal and their corresponding sides are within the same ratio (or proportion) such that area of these similar triangle will be in proportion to the square of their similar sides.
Calculations:
⇒ Area of ∆PQR/Area of ∆MNT = PR2/MT2
⇒ 196/169 = PR2/MT2
Taking square roots on both sides, we get
⇒ 14/13 = 28/MT
⇒ MT = 26 cm