Question : If the ratio of the perimeter of two similar triangles is 4:25, then the ratio of the areas is
a) 4:25
b) 25:4
c) 625:16
d) 16:625
Doubt by Zoha
Solution :
Let two two triangles by ΔABC and ΔPQR
ΔABC~ΔPQR (Given)
Perimeter (ΔABC) / Perimeter (ΔPQR) = 4:25
We know, the ratio of the perimeter of the similar triangles is the same as the ratio of their corresponding sides
Perimeter (ΔABC) / Perimeter (ΔPQR) = AB/PQ
4:25 = AB/PQ
4:25 = AB/PQ
AB/PQ = 4:25
We also know that, the ratio of the area of two similar triangle is equal to the square of the ratio their corresponding sides.
ar(ΔABC) / ar(ΔPQR) = (AB/PQ)2
ar(ΔABC) / ar(ΔPQR) = (4/25)2
ar(ΔABC) / ar(ΔPQR) = (4/25)2
ar(ΔABC) / ar(ΔPQR) = 16:625
Hence, d) would be the correct option.
Similar Question :
The perimeters of two similar triangles ΔABC and ΔPQR are 35 cm and 45 cm respectively, then the ratio of the area of the two triangles is _____________. [CBSE SQP 2019-2020]
Solution :
Perimeter (ΔABC) = 35 cm
Perimeter (ΔPQR) = 45 cm
Perimeter (ΔABC) / Perimeter (ΔPQR) = 35/45
Perimeter (ΔABC) / Perimeter (ΔPQR) = 7/9
Perimeter (ΔABC) / Perimeter (ΔPQR) = 7/9
Perimeter (ΔABC) / Perimeter (ΔPQR) = AB/PQ
7/9 = AB/PQ
7/9 = AB/PQ
AB/PQ = 7/9
ar(ΔABC) / ar(ΔPQR) = (AB/PQ)2
ar(ΔABC) / ar(ΔPQR) = (7/9)2
ar(ΔABC) / ar(ΔPQR) = (7/9)2
ar(ΔABC) / ar(ΔPQR) = 49:81
Practice Question :
The perimeter of two similar triangles ABC and XYZ are 60 cm and 48 cm respectively. If XY=8 cm the the length of AB would be
a) 4 cm
b) 6 cm
c) 8 cm
d) 10 cm
Click Here for the Answer
d) is the correct option