Question

The perimeter of an isosceles triangle is 44 cm and ratio of the 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 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 THEORAM IN 1 HALF OF THE ISOSCELES TRIANGLE AS FOR PYTHAGORAS THEORAM 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