In the given figure, AB CD EF,
given that AB=7.5 cm, DC=y cm
EF = 4.5 cm and BC = x cm, find
the values ofx and y.
Answers
Heya..........❤✌
Firstly, look at the given figure & note down the given values
AB||CD||EF
AB=7cm, CF= 3 cm, EF=4.5cm
DC=y cm &BC = x cm
Then, identify the similar triangles in the given figure.
Explanation : Angle ACB = Angle ECF
∠BAC = ∠FEC
∠ABC = ∠CFE
So, from AAA theorem, consider Triangle BCD & triangle BFE are similar triangles.
Hence, use the similar triangle properties
Note: the ratios of the lengths of similar triangles corresponding.
sides are equal.
Triangle ACB & CEF are similar
Hence, AB/EF = x/3
Triangle BCD & Triangle BEF are similar
So, BC/DC = BF/EF
Plugging the known values & simplify the unknown.... we get...
7.5 / 4.5 = x/3
=> x = 5
Now, to find y use the value of x
5/y = (5+3)/4.5
=> y = 45/ 16
Hope it’s helpful....... ☺
