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:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e 21 units
The sides of the triangle are given as 25, 34 & 39 then the area of the triangle is given as,
⇒ √{s(s - a)(s - b)(s - c)}
Where 's' is given as
⇒ s = (a + b + c) / 2
⇒ s = (25 + 34 + 39) / 2
⇒ s = 98 / 2 = 49
Area = √{49(49 - 25)(49 - 34)(49 - 39)}
Area = √{49 × 24 × 15 × 10}
Area = √{7 × 7 × 2 × 2 × 2 × 3 × 3 × 5 × 2 × 5}
Area = 7 × 2 × 2 × 3 × 5 = 420 unit2
Area of square will be = 420 + 21 = 441 unit2
Side = √441 = 21 units