The areas of two similar triangles ABC and PQR are 64 cm2 and 144 cm2, respectively. If the greatest side of the smaller △ABC is 24 cm, then what is the greatest side of the bigger △PQR?
Answer & explanation
Correct answer: option 4
Concept Used
The similarity of triangles = If two triangles are similar, then their corresponding angles are congruent and corresponding angles are congruent and corresponding sides are equal in proportion.
Ratio of area of similar triangles = (ratio of sides of the triangles)2
Calculations
Let the greatest side of the bigger \(\Delta \)PQR be x
Greatest side of the smaller \(\Delta \)ABC = 24 cm
According tot the question,
Ratio of the area of triangles = 64 : 144
As we know that
Ratio of the triangles = (ratio of sides of the triangles)2
= \(\frac{64}{144}\) = \(\frac{24}{x}\)2
= \(\frac{8}{12}\) = \(\frac{24}{x}\)
= x = 36 cm.
Therefore, greatest side of the bigger \(\Delta \)PQR is 36 cm.