Question:
The perimeters of two squares are 40 and 96 metres respectively. Find the perimeter of another square equal in area to the sum of the first two squares.
Solution:
From the question it is given that,
Perimeters of first squares = 40m
Perimeter of second square = 96m
Let us assume side of first square = x1
and assume side of second square = x2
WKT, perimeter of first square = 4 × side
40 = 4x1
X1 = 40/4
X1 = 10 m
Then,
Perimeter of second square = 4 × side
96 = 4x2
X2 = 96/4
X2 = 24 m
As per the condition given in the question area of another square is equal to the first two squares.
Let us assume y2 be the area of another square.
So,
y2 = x12 + x22
y2 = 102 + 242
y2 = 100 + 576
y = √(676)
y = 26 m
Then,
Perimeter of another square = 4 × side
= 4 × y
= 4 × 26
= 104 m