Question

Problem 4:
The hypotenuse of a right angled triangle is 20 cm. The difference between its other two sides is 4 cm. Find the length of the sides.

Answer 1

Answer:

12cm and 16cm

Step-by-step explanation:

The hypotenuse of the right angle triangle  = 20cm

 let the other two sides be x and y;

 The difference;

                x  = y - 4

Problem:

Find x and y;

Solution:

According to the pythagoras theorem;

    x² + y² = 20²  ------ i

       x² + y² = 400 ----- i

and  x - y = 4 ---- ii

So;   x = 4 + y

Now input the value into equation (i);

  (y + 4)² + y² = 400

   (y+4)(y+4) + y² = 400

    y² + y² + 4y + 4y + 16 = 400

    2y² + 8y + 16 = 400

    2y² + 8y + 16 -400 = 0

   2y² + 8y - 384 = 0;

      y² + 4y - 192 = 0

Factorize the equation;

  y² + 16y - 12y - 192 = 0

  y(y + 16) - 12(y + 16) = 0

  (y-12)(y + 16) = 0

     y -12 = 0 or y+ 16 = 0

     y = 12 or -16

It is not realistic for the length of a body to be a negative value, so y= 12;

   since;

    x - y = 4,

    x = 4 + 12

    x = 16