Question

The perimeter of an isosceles triangle is 44 cm, and the ratio of its equal side to its base is 4:3. The area of the triangle is

Answer 1

Answer:

The perimeter of isosceles triangle = 44 cm

Perimeter of isosceles triangle = 2 * Equal sides + base

Let the length of equal side be 4x and base be 3x

Then,       2 * 4x + 3x = 44cm

               8x + 3x = 44 cm

               11x = 44 cm

                x = 44/11 => 4 cm

Length of equal sides = 4 * 4 => 16 cm

Length of base = 3 * 4 => 12cm

TO FIND HEIGHT OF TRIANGLE WE WILL USE PYTHAGORAS THEOREM IN 1 HALF OF THE ISOSCELES TRIANGLE AS FOR PYTHAGORAS THEOREM WE NEED RIGHT ANGLED TRIANGLE ..... Then base = 12 / 2 => 6 cm.

                    (Hypotenuse)^2 = base^2 + height^2

                     16 * 16 = 6* 6 + (height)^2

                     256 = 36 + (height)^2

                    256 - 36 = (height) ^2

               220 = height^2

               √220 = height of triangle

   NOW

AREA OF TRINGLE = 1/2 * base * height

                               = 1/2 * 12 *  √220

                               = 6 * √220

                               = 6 * 2√55                                                                   

      ANSWER ====> 12 √55 sq. cm

Step-by-step explanation:

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