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

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.