Question

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.

Answer 1

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: