Question

If the difference between the sides of a right angled triangle is 3 cm its area is 54 centimetre square find its perimeter​

Answer 1

Answer:

Step-by-step explanation:

Let the two sides be x and x + 3

Area = 54 cm^2

1/2 (x)(x+3) = 54

x² + 3x = 108

x² + 3x - 108 = 0

(x+12)(x-9) = 0

x = 9

Sides are 9 cm and 12 cm

Hypotenuse =  

               

                   =  

                   =  

 

                  = 15 cm

Perimeter of triangle = 9 + 12 + 15 = 36  cm

thx...

Answer 2

Given :-

• Difference between the sides of a right angled triangle is 3 cm.
• Area = 54cm²

To find :-

• Perimeter = ?

Solutions :-

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.

We know that :-

• Area of triangle = 1/2 × Base × Height = 54cm²

Now,

→ 1/2 * x * ( x + 3 ) = 54

= x² + 3x = 108

→ x² + 12x - 9x - ( 12 * 9 ) = 0

Solving it x=9;−12

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

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

→ AC = x + 3 = 12cm

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

Hence, BC = 15cm

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