Answer:
Let's denote the length of the rectangle as
�
L meters and the breadth as
�
B meters.
According to the given information, the breadth is 3 meters less than its length, so
�
=
�
−
3
B=L−3.
The perimeter (
�
P) of a rectangle is given by the formula
�
=
2
(
�
+
�
)
P=2(L+B).
Given
�
=
26
P=26 meters:
26
=
2
(
�
+
(
�
−
3
)
)
26=2(L+(L−3))
Now, simplify and solve for
�
L:
26
=
2
(
2
�
−
3
)
26=2(2L−3)
26
=
4
�
−
6
26=4L−6
4
�
=
32
4L=32
�
=
8
L=8
Now that we know the length (
�
L) is 8 meters, we can find the breadth (
�
B):
�
=
�
−
3
B=L−3
�
=
8
−
3
B=8−3
�
=
5
B=5
5
Now, we can find the diagonal (
�
D) of the rectangle using the Pythagorean Theorem:
�
=
�
2
+
�
2
D=
L
2
+B
2
�
=
8
2
+
5
2
D=
8
2
+5
2
�
=
64
+
25
D=
64+25
�
=
89
D=
89
So, the length of the diagonal is
89
89
meters.