Mathematics
Given: ∠GHE = ∠DFE = 90°, DH = 8, DF = 12, DG = 3x – 1 and DE = 4x + 2.
Find: the lengths of segments DG and DE.
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Answer
In ΔDHG and ΔDFE,
⇒ ∠GHD = ∠DFE = 90°
⇒ ∠D = ∠D [Common]
Thus, ∆DHG ~ ∆DFE [By AA]
Since, corresponding sides of similar triangles are proportional we have :
DG = 3x - 1 = 3(7) - 1 = 21 - 1 = 20,
DE = 4x + 2 = 4(7) + 2 = 28 + 2 = 30.
Hence, DG = 20 and DE = 30.
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