If the difference between the sides of a rightangled triangle is 3 cm

1.	If the difference between the sides of a rightangled triangle is 3 cm and its area is 54 cm²;find its perimeter.
Answer» the DIFFERENCE between the BASE and height is 3cm3cm, let AB =xcm=xcm and AC =(x+3)CM=(x+3)cm Area of triangle =12×base×height=54=12×base×height=54 sq cm 12×x×(x+3)=5412×x×(x+3)=54 =>x2+3x=108=>x2+3x=108 x2+12x−9x−(12×9)=0x2+12x−9x−(12×9)=0 Solving it x=9;−12x=9;−12 Since SIDE cannot be negative, AB =x=9cm=x=9cm AC =x+3=12cm=x+3=12cm Since the third side BC is the hypotenuse , BC2=92+122=225BC2=92+122=225 Hence, BC =15cm=15cm Perimeter of the triangle == Sum of all sides =15+9+12=36cm=15+9+12=36cm

If the difference between the sides of a rightangled triangle is 3 cm and its area is 54 cm²;find its perimeter.

Answer»

the DIFFERENCE between the BASE and height is 3cm3cm, let AB =xcm=xcm and AC =(x+3)CM=(x+3)cm

Area of triangle =12×base×height=54=12×base×height=54 sq cm

12×x×(x+3)=5412×x×(x+3)=54

=>x2+3x=108=>x2+3x=108

x2+12x−9x−(12×9)=0x2+12x−9x−(12×9)=0

Solving it x=9;−12x=9;−12

Since SIDE cannot be negative, AB =x=9cm=x=9cm

AC =x+3=12cm=x+3=12cm

Since the third side BC is the hypotenuse , BC2=92+122=225BC2=92+122=225

Hence, BC =15cm=15cm

Perimeter of the triangle == Sum of all sides =15+9+12=36cm=15+9+12=36cm