Question
Download Solution PDFIn the figure given below, ∠AED = ∠BAC, AD || BC, AD : BC = 7 : 9 and AC = 36 cm, then find the length of EC.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGIVEN:
∠AED = ∠BAC
AD || BC
AD : BC = 7 : 9
AC = 36 cm
CONCEPT:
Similarity of triangle
CALCULATION:
Since ∠AED = ∠BAC
∠EAD = ∠ACB (alternate interior angle)
Rule of similarity AA(Angle-Angle)
∆EDA and ∆ABC are similar.
Now,
AD/BC = AE/AC
⇒ 7/9 = AE/36
⇒ AE = 28 cm
Now,
EC = AC – AE = 36 – 28 = 8 cm
∴ The value of EC is 8 cm
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