Question
Download Solution PDFΔABC ∼ ΔEDF and area (ΔABC) :area (ΔEDF) = 1 : 4. If AB = 7 cm, BC = 8 cm and CA = 9 cm, then DF is equal to:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
ΔABC ~ ΔEDF,
AB = 7 cm,
BC = 8 cm,
CA = 9 cm and ar(ΔABC) ∶ ar(ΔEDF) = 1/4
Concept used:
When two triangles are similar then the ratio of their area is equal to the ratio of the square of their corresponding sides.
Calculation:
As we know,
ar(ΔABC) / ar(ΔEDF) = (BC/DF)2 (As the triangles are similar)
⇒ 1/4 = 82/DF2
⇒ DF2 = 82 × 4
⇒ DF = 8 × 2 = 16 cm
∴ DF is equal to 16 cm.
Last updated on May 28, 2025
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