Question
Download Solution PDFΔABC and ΔDEF are similar triangles, and their areas are 81 cm2 and 144 cm2, respectively. If EF = 20 cm, then what is the value of BC?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
ΔABC and ΔDEF are similar triangles
Area of ΔABC = 81 cm2
Area of ΔDEF = 144 cm2
EF = 20 cm
Formula used:
For similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides.
\(\dfrac{Area\ of\ ΔABC}{Area\ of\ ΔDEF}\) = \(\left(\dfrac{BC}{EF}\right)^2\)
Calculation:
\(\dfrac{81}{144}\) = \(\left(\dfrac{BC}{20}\right)^2\)
⇒ \(\dfrac{9}{12}\) = \(\left(\dfrac{BC}{20}\right)\)
⇒ \(\dfrac{3}{4}\) = \(\dfrac{BC}{20}\)
⇒ BC = \(\dfrac{3}{4} \times 20\)
⇒ BC = 15
∴ The correct answer is option (1).
Last updated on May 28, 2025
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