Question

The highpotenuse of a right triangle is 25cm and its perpendicular distance is 7cm.. Find the length of its base.

Answer 1

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Answer 2

The length of the base is 24 cm.

Given: The hypotenuse of a right triangle is 25 cm and its perpendicular distance is 7 cm.

To Find: the length of the base.

Solution:

• Whenever we are given a right-angled triangle, we can find the length of its sides by implementing the Pythagoras theorem.

• The Pythagoras theorem states that the square of the hypotenuse is equal to the sum of the squares of the length of the base and perpendicular.

• It can be shown by;

        ( Hypotenuse )²  =  ( Base )² + ( Perpendicular )²                ....(1)

Coming to the numerical, we are given;

The length of the hypotenuse = 25 cm

The length of the perpendicular = 7 cm

So, by putting respective values in (1), we have;

          ( Hypotenuse )²  =  ( Base )² + ( Perpendicular )²  

     ⇒  ( 25 )²  =  ( Base )² + ( 7 )²

     ⇒  625    =   ( Base )²  +  49

     ⇒  ( Base )²  =  625 - 49

     ⇒  ( Base )²  = 576

     ⇒   Base  =  √576

                      = 24 cm

Hence, the length of the base is 24 cm.

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