Geometry Math Problem: Find the length of the hypotenuse
Find the length of the hypotenuse of a triangle which is extended from the side of another right triangle
APQ is a triangle with sides 3 cm,4 cm, and 5 cm
Solution
Extend AP and draw a perpendicular line to AB which is passing through B and form another triangle ABQ
Then find the length of the AB
Let PC = x
From figure hypotenuse of the triangle = PA + PC = 3 + x
Apply Pythagoras theorem in triangle APB
BC² = AC² – AB² = (3 + x)² – 5²……………….eq(1)
Apply Pythagoras’ theorem in triangle BPC
BC² = BP² + PC² = 4² – x²……………………..eq(2)
(3 + x)² – 5² = 4² – x²
⇒ 9 + 6x + x² – 25 = 16 + x²
⇒ 6x = 32
⇒ x = 16/3 cm
So, Hypotenuse of the right triangle = 3 + 16/3 = 25/3 cm
