The perimeter of an isosceles triangle is 42 cm and its base is (3/2) times each of the equal sides.find the length of each side if the triangle,area of the triangle and the height of the truangle.
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Let the sides of the triangle be a,a,b
perimeter of an isosceles triangle = a+a+b
a+a+ 3/2 a = 42
⇒ a = 12 cm
∴ b = 3/2 * 12 = 18 cm
The altitude of an isosceles triangle would divide the triangle to right triangle.
In a right Δ, hypotenuse = √base² + altitude²
12² = 9² + x²
⇒ x = 3√7 cm
area of triangle = 1/2 *base * height
= 1/2 * 18 * 3√7
= 27√7 cm
perimeter of an isosceles triangle = a+a+b
a+a+ 3/2 a = 42
⇒ a = 12 cm
∴ b = 3/2 * 12 = 18 cm
The altitude of an isosceles triangle would divide the triangle to right triangle.
In a right Δ, hypotenuse = √base² + altitude²
12² = 9² + x²
⇒ x = 3√7 cm
area of triangle = 1/2 *base * height
= 1/2 * 18 * 3√7
= 27√7 cm
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