SOLUTION: Two sides of a triangle are 26 and 27, while the height to the third side is 25. Find the area of the triangle

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Question 1180830: Two sides of a triangle are 26 and 27, while the height to the third side is 25. Find the area of the triangle
Answer by ikleyn(52781) About Me  (Show Source):
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Under given description, two cases are possible.



Case 1.  The altitude of 25 cm lies BETWEEN the sides of 26 cm and 27 cm.

         In this case, the altitude divides the third side in two parts.         

         The length of one part is  sqrt%2826%5E2-25%5E2%29 = sqrt%2851%29 cm.

         The length of other part is  sqrt%2827%5E2-25%5E2%29 = sqrt%28104%29 cm.

         Thus the base of the triangle is the sum  sqrt%2851%29%2Bsqrt%28104%29 cm.


         Having the base and the altitude, the area of the triangle is


                area = %281%2F2%29%2A%28sqrt%2851%29%2Bsqrt%28104%29%29%2A25 = 216.743 cm^2 (rounded)     ANSWER



Case 2.  Both sides of 26 cm and 27 cm lie on the same side of the 25-cm altitude.


         In this case, the base of the triangle is the DIFFERENCE  sqrt%28104%29-sqrt%2851%29 cm.


         Having the base and the altitude, the area of the triangle is in this case


                area = %281%2F2%29%2A%28sqrt%28104%29-sqrt%2851%29%29%2A25%29 = 38.207 cm^2 (rounded)     ANSWER

Solved, answered and carefully explained.


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