Answer:
c = √29
Step-by-step explanation:
The Pythagorean theorem tells you the sum of the squares of the legs is the square of the hypotenuse.
Application
Each corner triangle has legs of 2 and 5, and hypotenuse 'c'.
2² +5² = c²
c² = 4 +25 = 29
c = √29
The value under the radical is 29.
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Alternate solution
The four triangles have a total area of ...
A = 4(1/2)(bh) = 2bh = 2(5)(2) = 20
The overall square has an area of ...
A = s² = (2 +5)² = 49
Then the area of the square whose side length is 'c' is ...
smaller square area = c² = 49 -20 = 29
Taking the square root gives ...
c = √29
