Maths-
General
Easy
Question
The lengths of the two sides of right triangle containing the right angle differ by 2 cm. If the area of triangle is 24 cm2. Find the perimeter of triangle
Hint:
Sides containing right angle are height and base.
The correct answer is: 24 cm
It is given that difference between perpendicular and base = 2 cm
i.e. b – h = 2 ⇒ b = 2 + h
Now, Area of triangle = 24 cm2
= 24
= 48
h2 + 2h – 48 = 0
h = ![fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction](data:image/png;base64,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)
h = ![fraction numerator negative 2 plus-or-minus square root of 2 squared minus 4 left parenthesis negative 48 right parenthesis end root over denominator 2 end fraction equals fraction numerator negative 2 plus-or-minus square root of 196 over denominator 2 end fraction equals fraction numerator negative 2 plus-or-minus 14 over denominator 2 end fraction](data:image/png;base64,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)
h = 6 , - 8
Since, perpendicular is always positive so h = 6
Base, B = 2 + 6 = 8
Using Pythagoras theorem ,
H2 = B2 + P2
H2 = 82 + 62 = 64 + 36 = 100
H =
= 10 cm
Perimeter of triangle = Sum of all sides
= 8 + 10 + 6 = 24 cm
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