In a right angle triangle, length of hypotenuse is 12cm more than its shortest side. The length of other side is 6cm less than the hypotenuse then find the side of right angle triangle.
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Le the smalest side AB be x cm
Hypotenuse AC = x+ 12
Other side BC = x +12 -6
= x + 6
From Pythagoras theorem
AC square= AB square + BC square
(x+12)sq =(x)sq + (x+6)sq
Using identity (a + b) sq= a sq + 2 ab + b sq
x sq +24 x +144 = x sq +x sq+ 12x +36
24x +144= x sq+ 12x +36
0=x sq +12x -24x +36 -144
0= x sq -12x -108
Spliting the middle term
0= x sq +24x -12x - 108
0=x(x+ 24) -12(x+24)
0=( x-12) (x+24)
x= 12; -24
Since, sides cannot be negative
Therefore,
AB=12cm
AC=24 cm
BC=18cm
Step-by-step explanation:
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