A triangle has sides 25, 39, 34 units. If the area of a square exceeds the area of this triangle by 21 units, then the side of the square is:
Answer & explanation
Correct answer: option 2
We know that,
Area of a triangle = \(\sqrt {s(s-a)(s-b)(s-c) }\)
and semi perimeter = \(\frac{a + b + c}{2}\)
Sides of triangle = 25, 39 and 34 units.
a = 25
b = 39
c = 34
Area of square is more than that of triangle = 21 units
Semi perimeter = \(\frac{25 + 39 + 34}{2}\) = 49
Area of a triangle = \(\sqrt {49(49-25)(49-39)(49-34)}\)
= \(\sqrt {49(24)(10)(15)}\)
= \(\sqrt {176400}\) = 420
Area of square = 420 + 21 = 441
Side of square = \(\sqrt {441}\) = 21 unit