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Question

Three pieces of garden Edging measure 20cm ,41cm and 44cm. If the same length is cut of each pieces the remaining length can be formed into the right triangle. What length is cut off.

Answer 1

Three pieces of garden Edging of garden

20 cm , 41 cm and 44 cm.

Let cut off length = x cm

If the same length is cut of each pieces the remaining length can be formed into the right triangle.

One side = 20 - x

Another side = 41 - x

Hypotenuse = 44 - x

(one side)² + (another side)² = ( hypotenuse )²

(20 - x)² + (41 - x)² = ( 44 - x )²

(400 - 40x + x² )+ (1681 -82x + x² ) = ( 1936 - 88x + x² )

(400 - 40x + x² )+ (1681 -82x + x² ) - ( 1936 - 88x + x² ) = 0

( x² + x² - x² ) + ( 40x - 82 x + 88x ) + ( 400 + 1681 - 1936 ) = 0

x² + -34x + 145 = 0

For factoring above equation, appropriate factor is 145 = 29×5

x²  - 29x - 5x - 192 = 0

x ( x - 29 ) - 5 ( x - 29 ) = 0

( x - 29 ) ( x - 5 ) = 0

By using zero product property : If AB = 0 then A = 0 , B = 0

( x - 29 ) = 0  and  ( x - 5 ) = 0

( x - 29 ) = 0 then x = 29 is invalid.Since 20 cm side become negative.It is meaningless.

( x - 5) = 0 then  x = 5 cm is valid.

Solution :

Cut off piece length of garden is 5 cm