Question

In the given figure, m/GHE = mDFE = = 90°. If DH = 8 cm, DF = 12 cm, DG = (3x- 1) cm and DE = = (4x + 2) cm, find the length of DG and DE. G E D H (A) 16 cm, 24 cm (B) 20 cm, 30 cm (C) 23 cm, 50 cm (D) 34 cm, 35 cm​

Answer 1

Answer:

ans.B

Step-by-step explanation:

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Answer 2

Here we can make two seperate right angled traingles as shown above.

Now let's prove that: ∆EFD ≈ ∆GHD

angle F= angle H (both 90°)

angle EDF= angle EDH (common angle)

hence

∆EDF ≈ ∆GHD (by AA property)

Now by CPCTC,

$\frac{ef}{gh} = \frac{fd}{dh} = \frac{ed}{gd}$

$i.e. \: \: \frac{12}{8} = \frac{4x + 2}{3x - 1}$

$12(3x - 1) = 8(4x + 2)$

$36x - 12 = 32 x + 16$

$36x - 32x = 16 + 12$

$4x = 28$

$x = 7$

Thus,

ED = 4x+2 = 4×7+2 = 28+2 = 30 cm

GD = 3x-1 = 3×7-1 = 21-1 = 20 cm

Hence,

Option (B) 20 cm, 30 cm is correct

Hope it helps:)