Answer:
√41
Explanation:
Considering the sides with lengths 48 and 52 units, we would use Pythagoras theorem to find the third side. Let that side be t
52² = 48² + t²
t² = 52² - 48²
= 2704 - 2304
= 400
t = √400
= 20
Considering the next triangle with sides t (20 units) and 12 units, again using the theorem
20² = 12² + y²
where y is the third side
400 = 144 + y²
y² = 400 - 144
= 256
y = √256
= 16 units
Considering the triangle with two sides given as 5 and 13 units, the third side (which is part of the 16 units calculated earlier)
13² = 5² + u²
where u is the 3rd side
169 = 25 + u²
u² = 169 - 25
u² = 144
u = √144
u = 12
The other part of the side of that triangle
= 16 - 12
= 4
Considering the smallest triangle whose sides are x, 5 and 4,
x² = 5² + 4²
= 25 + 16
= 41
x = √41