Question

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Answer 1

GF = 11, GE = 28, HF = 14,
`DG=5\sqrt3`

Solution:

Given data:

DE = 11, GH = 14

In rectangle, opposite sides are equal.

DE = GF

GF = 11

Property of a rectangle:

The diagonals of a rectangle are equal in length and they bisect each other.

Half of diagonal GE = GH = 14

GE = 2 × GH

= 2 × 14

GE = 28

HF is also a half of the diagonal DF.

By property of a rectangle, GH = HF

HF = 14

Diagonal of a rectangle formula:

`D=\sqrt{\text{length}^2+\text{breadth}^2}`

`14=√(DG^2+11^2)`

Squaring on both sides, we get

`196={DG^2+121}`

`{DG^2=196-121}`

`{DG^2=75}`

Taking square root on both sides, we get

`DG=5\sqrt3`

Hence GF = 11, GE = 28, HF = 14,
`DG=5\sqrt3`.