if the area of the right angle triangle formed by two in adjacent sides of a diagonal of a square is 40.5 square metre then find the perimeter of the square
Since the diagonal of a square is the hypotenuse of a right-angled triangle formed by two adjacent sides, we can calculate the length of the diagonal using the Pythagorean Theorem:
d
2
=
s
2
+
s
2
where d=length of the diagonal and s=length of a side.
Answers & Comments
Step-by-step explanation:
The formula for area of a square is:
s
2
=
A
where A=area and s=length of a side.
Hence:
s²=81
s
=
√
81
Since
s
has to be a positive integer,
s
=
9
Since the diagonal of a square is the hypotenuse of a right-angled triangle formed by two adjacent sides, we can calculate the length of the diagonal using the Pythagorean Theorem:
d
2
=
s
2
+
s
2
where d=length of the diagonal and s=length of a side.
d
2
=
9
2
+
9
2
d
2
=
81
+
81
d
2
=
162
d
=
√
162
d
=
12.73
Step-by-step explanation:
See
1/2 (side)^2 = 40.5
(side)^2 = 90
side = √(90) = 3√10
so required perimeter is 4(side)
= 4(3√10)
= 12√10
ans