GF = 11, GE = 28, HF = 14, [tex]DG=5\sqrt3[/tex]
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:
[tex]D=\sqrt{\text{length}^2+\text{breadth}^2}[/tex]
[tex]14=\sqrt{DG^2+11^2}[/tex]
Squaring on both sides, we get
[tex]196={DG^2+121}[/tex]
[tex]{DG^2=196-121}[/tex]
[tex]{DG^2=75}[/tex]
Taking square root on both sides, we get
[tex]DG=5\sqrt3[/tex]
Hence GF = 11, GE = 28, HF = 14, [tex]DG=5\sqrt3[/tex].
