Question

the perimeter of isosceles triangle triangle is 44cm and the ratio of . the equal side. to its base is 4:3 the area of 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 the height of the triangle, we will use Pythagoras Theorem in 1 half of the Isosceles triangle as for the Pythogoras Theorem we need the 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