Question

The perimeter of an isosceles triangle is 42 cm and its base is (3/2) times each of equal sides. find the length of each side of the triangle, area of the triangle amd the height of the triangle​

Answer 1

Let the length of the equal sides be "a".

Then, perimeter = a + a + (3/2)*a

But the perimeter is 42cm. Therefore,

42 = 2a + 3a/2 = (4a + 3a)/2 = 7a/2

Therefore a = 42 * 2 / 7 = 12 cm.

The equal sides are 12 and the base is (3/2)*12 = 18.

To find the height, we will have to use Pythagoras theorem with the hypotenuse being 12 and base being 18/2 = 9.

Then, the height = sqrt (12^2 - 9^2) = sqrt [(12+9)*(12-9)] = sqrt(21*3)

= sqrt 63 = 7.937 or 7.94cm.

Therefore, area of the triangle = (1/2)*7.94*9 = 35.73 sq. cm.

Thus,

a. Length of each side of the triangle is 12cm, 12cm and 18cm
b. Area of the triangle = 35.73 sq. cm.
c. Height of the triangle = 7.94cm.