Question

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

Answer 1

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