Question

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 of the triangle. Also find the area of the triangle and its height

Answer 1

let the sides be x
=>x+x+3/2x=42cm
2x+3/2x=42
=>7/2x=42
=>x=42×2/7
= x=12cm
and 3/2x=3/2×12=18cm

ans:12cm and 18cm

Answer 2

let 'x' be the measure of its equal side,
Base =(3/2)x
Since x+x+(3/2)x=42
(7/2)x=42
or x =12cm
Therefore sides are 12cm,12cm and 18cm
Now s=(a+b+c)/2 =42/2= 21cm
Area of Triangle =square root of s (s-a)(s-b)(s-c)
= square root of 21 (21-12)(21-12)(21-18)
or, Area of triangle = 71.42 cm^2
Since Area of Triangle =71.42 cm^2
(1/2)×18×h = 71.42
or, h= 7.93 cm