In the given figure, A ABC is similar to
A DEF, AB = (x - 0-5) cm, AC = 1.5x cm,
DE
9 cm, and DF = 3x cm. Find the
lengths of AB and DF.
Answers
Given : ΔABC similar to ΔDEF
AB = ( x - 0.5) cm
AC = 1.5x cm
DE = 9 cm
DF = 3x cm
To Find : lengths of AB and DF.
Solution:
ΔABC ~ ΔDEF
Corresponding sides of similar triangles are proportional
Hence Their ratio is constant
AB/DE = AC/DF
=> (x - 0.5)/9 = 1.5x/3x
=> (x - 0.5)/9 = 1/2
=> 2x - 1 = 9
=> 2x = 10
=> x = 5
AB = ( x - 0.5) = 5 - 0.5 = 4.5 cm
AC = 1.5x = 1.5 * 5 = 7.5 cm
DE = 9 cm
DF = 3x = 3 * 5 = 15 cm
Length of AB = 4.5 cm
Length of DF = 15 cm
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Answer:
Triangle ABC ~ TriangleDEF
Corresponding sides of similar triangles are proportional
Hence Their ratio is constant
AB/DE = AC/DF
=> (x -0.5)/9 = 1.5x/3x
=> (x -0.5)/9 = 1/2
=> 2x-1=9
=> 2x = 10
=> x = 5
AB = (x -0.5) = 5 -0.5 = 4.5 cm
AC = 1.5x = 1.5 * 5 = 7.5 cm
DE = 9 cm
DF = 3x = 3 * 5 = 15 cm
Length of AB = 4.5 cm
Length of DF = 15 cm.