A right angled triangle of area 600 m2 is to be made such that the hypotenuse is double the base. For the triangle, the hypotenuse is ___________ more than the base.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 26.32 m.
Area of a triangle = (1/2) × Base × height
⇒ 600 = (1/2)bh
⇒ h = 1200/b
In a right-angled triangle, hypotenuse2 = base2 + height2
(2b)2 = b2 + h2
⇒ 4b2 = b2 + h2
⇒ 4b2 = b2 + (1200/b)2
⇒ 3b2 = 1440000/b2
⇒ b4 = 1440000/3 = 480000
⇒ b = 26.32 m (approx)
Therefore, the hypotenuse is 26.32 meters more than the base.