Question
Download Solution PDFA 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.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Area of the right-angled triangle = 600 m2
Hypotenuse = 2 × Base
Hypotenuse > Base
Formula used:
Area of right-angled triangle = (1/2) × Base × Height
Pythagoras theorem: Hypotenuse2 = Base2 + Height2
Calculation:
Let the base be b meters.
Height = h meters.
Hypotenuse = 2b meters.
Area = (1/2) × b × h
600 = (1/2) × b × h
⇒ h = 1200 / b
Using Pythagoras theorem:
(2b)2 = b2 + (1200 / b)2
⇒ 4b2 = b2 + 1440000 / b2
⇒ 3b4 = 1440000
⇒ b4 = 480000
⇒ b2 = 692.82
⇒ b = 26.32 m
Hypotenuse = 2 × 26.32 = 52.64 m
Difference between hypotenuse and base = 52.64 - 26.32 = 26.32 m.
Therefore, hypotenuse is 26.32 m more than the base.
∴ The correct answer is option 2.
Last updated on May 28, 2025
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