Question

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

Answer 1

let equal sides of isosceles triangle be 'x'
Then third side=3x/2
perimeter of isosceles triangle=42
x+x+3x/2=42
2x+2x+3x=84
x=12
Therefore sides of isosceles triangle=12,12,3×12/2=12,12,18
We know that the median and altitude of equilateral triangle and isosceles triangle are same.
Construct a altitude on unequal side of isosceles triangle.
Now it get divided into two equal parts i.e 9,9cm
By applying pythagoras theorem we get,
12^2=9^2+height^2
height=√63=3√7
Area of isosceles triangle=1/2×b×h
=1/2×18×3√7
=27√7cm^2
Hence sides of isosceles triangle are 12cm,12cm,18cm ,height of this triangle is equals to 3√7cm , and area of this triangle is equals to 27√7cm^2.