Question

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

Answer 1

Answer:

Let ABC be the right angled triangle with right angle at A.

AB is the base, AC is the height and BC is the hypotenuse.

As the difference between the base and height is 3cm, let AB =xcm and AC =(x+3)cm

Area of triangle =

2

1

×base×height=54 sq cm

2

1

×x×(x+3)=54

=>x

2

+3x=108

x

2

+12x−9x−(12×9)=0

Solving it x=9;−12

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

AC =x+3=12cm

Since the third side BC is the hypotenuse , BC

2

=9

2

+12

2

=225

Hence, BC =15cm

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

Answer 2

Step-by-step explanation:

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