A :-) 1.) Given - base = 9 cm height ( alt ) = 12 cm hypotenuse ( hypo ) = x Solution - By Pythagorus theorem ( hypo )^2 = ( base )^2 + ( alt )^2 ( x )^2 = ( 9 )^2 + ( 12 ) ^2 ( x )^2 = 81 + 144 ( x )^2 = 225 ( x ) = _/225 ( x ) = 15 cm
.:. The value of x ( hypotenuse ) = 15 cm
2.) Given - base = 10 cm Height = 24 cm Hypotenuse = x Solution - By pythagorus theorem ( hypo )^2 = ( base )^2 + ( alt )^2 ( x )^2 = ( 10 )^2 + ( 24 )^2 ( x )^2 = 100 + 576 ( x )^2 = 676 ( x ) = _/676 ( x ) = 26
.:. The value of x ( hypotenuse ) = 26 cm
3.) Given - base = 3 cm Height = 7 cm Hypotenuse = x Solution - By pythagorus theorem ( hypo )^2 = ( base )^2 + ( alt )^2 ( x )^2 = ( 3 )^2 + ( 7 )^2 ( x )^2 = 9 + 49 ( x )^2 = 58 ( x ) = _/58 ( x ) = 7.6
.:. The value of x ( hypotenuse ) = 7.6 cm
4.) Given - base = 10 cm Height = 6 cm Hypotenuse = x Solution - By pythagorus theorem ( Hypo )^2 = ( base )^2 + ( alt )^2 ( x )^2 = ( 10 )^2 + ( 6 )^2 ( x )^2 = 100 + 36 ( x )^2 = 136 ( x ) = _/136 ( x ) = 11.6
.:. The value of x ( hypotenuse ) = 11.6 cm
5.) Given - hypotenuse = 24 cm height = 6 cm Base = x Solution - By pythagorus theorem ( hypo )^2 = ( base )^2 + ( alt )^2 ( 24 )^2 = ( x )^2 + ( 6 )^2 ( x )^2 = ( 6 )^2 - ( 24 )^2 ( x )^2 = 36 - 576 ( x )^2 = -540 ( x ) = _/-540 ( x ) = 23.2
.:. The value of x ( base ) = 23.2 cm
6.) Given - base = 1 cm height = 1 cm hypotenuse = x Solution - By pythagorus theorem ( hypo )^2 = ( base )^2 + ( alt )^2 ( x )^2 = ( 1 )^2 + ( 1 )^2 ( x )^2 = 1 + 1 ( x )^2 = 2 ( x ) = _/2 ( x ) = 1.4
.:. The value of x ( hypotenuse ) = 1.4 cm
7.) Given - hypotenuse = 21 cm height = 8 cm Base = x Solution - By pythagorus theorem ( hypo )^2 = ( base )^2 + ( alt )^2 ( 21 )^2 = ( x )^2 + ( 8 )^2 441 = ( x )^2 + 64 ( x )^2 = 64 - 441 ( x )^2 = -377 ( x ) = _/-377 ( x ) = 19.4
.:. The value of x ( base ) = 19.4
8.) given - height = 24 cm Hypotenuse = 30cm Base = x Solution - By pythagorus theorem ( hypo )^2 = ( base )^2 + ( alt )^2 ( 30 )^2 = ( x )^2 + ( 24 )^2 900 = ( x )^2 + 576 ( x )^2 = 576 - 900 ( x )^2 = -324 ( x ) = _/-324 ( x ) = 18
.:. The value of x ( base ) = 18 cm
9.) ( i ) lets find ‘x’ Given - base = 9 cm height = 5 cm hypotenuse = x Solution - By pythagorus theorem ( hypo )^2 = ( base )^2 + ( alt )^2 ( x )^2 = ( 9 )^2 + ( 5 )^2 ( x )^2 = 81 +25 ( x )^2 = 106 ( x ) = _/106 ( x ) = 10.2
.:. The value of x ( hypotenuse ) = 10.2 cm
( ii ) lets find ‘y’ Given - base = 3 cm height = 5 cm Hypotenuse = y Solution - By pythagorus theorem ( hypo )^2 = ( base )^2 + ( alt )^2 ( y )^2 = ( 3 )^2 + ( 5 )^2 ( y )^2 = 9 + 25 ( y )^2 = 34 ( y ) = _/34 ( y ) = 5.8
