Join 60,000+ competitive exam aspirants
or with email
Your Cart
SubtotalтВ╣0
TotalтВ╣0
Examoogle тАв User тАв info@examoogle.com тАв EE-2024-8821
Chapter 1 of 12 тАв Page 1 of 248ЁЯФТ Protected PDF тАв Watermarked
Join 60,000+ competitive exam aspirants
49:18
45:18
49:81
49:27 Question ID : 441009602848 Option 1 ID : 4410092366511 Option 2 ID : 4410092366509 Option 3 ID : 4410092366510 Option 4 ID : 4410092366512 Status : Answered Chosen Option : C
49:81
When two triangles are similar, the ratio of their areas is simply the square of the ratio of their corresponding sides. Just square the given ratio: 72=49 and 92=81.
Triangle ABC is similar to triangle PQR, and the ratio of their corresponding sides AB:PQ = 7:9.
Area(тЦ│PQR)Area(тЦ│ABC)тАЛ=(PQABтАЛ)2
When two triangles are similar, the ratio of their areas is simply the square of the ratio of their corresponding sides. Just square the given ratio: 72=49 and 92=81.
Students often forget to square the ratio, choosing the original ratio 7:9 or incorrectly calculating the squares (e.g., 72=14 instead of 49).
Recall the Area-Similarity Property
For any two similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides.
Area2тАЛArea1тАЛтАЛ=(side2тАЛside1тАЛтАЛ)2
Substitute the given values
We are given the ratio of corresponding sides AB:PQ=7:9. Plugging this into the formula gives:
Area(тЦ│PQR)Area(тЦ│ABC)тАЛ=(97тАЛ)2
Calculate the final ratio
Squaring both the numerator and the denominator, we get 72=49 and 92=81.
8149тАЛ
C is correct because the ratio of the areas of similar triangles is the square of the ratio of their corresponding sides, which is (7/9)2=49/81.
This property also extends to 3D shapes: if two solids are similar, the ratio of their volumes is the cube of the ratio of their corresponding linear dimensions (k3).
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download тАв 100K+ Aspirants