A wire is 112cm long is bent to form a right triangle.If the hypotenuse is 50cm long find the area?

Asked by 2806rahul | 25th Oct, 2010, 12:00: AM

Expert Answer:

Dear Student,
 
Let one of the perpendicular sides be A units.
 
Therefore the other side is B which is obtained as followes
 
A + B + 50 = 112
=> B = 112 - 50 - A = 62 - A units.
(As the perimeter of the triangle is the length of the wire.)
 
 
Also, since it is a right angle triangle, we must have
 
502 = A2 + B2
 
=> 2500 = A2 + (62 - A)2
 
=> 2500 = A2 + 3844 + A2 - 124A
 
=> 2A2 - 124A + 1344 = 0
 
=> A2 - 62A + 772 = 0
 
=> 62A - A2 = 772           (1)
 
 
Now, Area of the right triangle = 0.5 x A x B = 0.5 x A x (62 - A)
 
= 0.5 x (62A - A2)
 
= 0.5 x 772    (from 1)
 
= 386 sq units
 
 
 
Regards Topperlearning.

Answered by  | 25th Oct, 2010, 11:03: PM

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