Question

find the area of an isosceles triangle with perimeter 36 cm and base 16 cm

Answer 1

the the sides be x

2x+16=36
2x=30
x=15

find the area using herons formula


i kinda forget it

Answer 2

perimeter=36cm, 
base=16cm,
 ATQ,
          In an isosceles triangle there, is 2 equal sides with equal lenth and one random base, therefore the formula for the perimeter of an isosceles triangle should be:
                 perimeter= side1+side2+base=2*side(equal in isosceles triangle)+base
                           36 = 2*side+16
                      => 36-16= 2*side
                      => 20= 2*side
                      => side= 20/2
                 therefore, side= 10
Now,
    draw a line dividing the base in 2 equal parts starting form the common angle between the isosceles lines and that will be our height for the isosceles triangle.
NOTE THAT WHILE CALCULATING THE HEIGHT BY pythagoras theorem  BASE WILL BE DIVIDED BY 2
      Now, by pythagoras theorem:
                 in the sub/interior trinagle 
                 => (base/2)^2+(height)^2= (side)^2
                 =>(16/2)^2+ height^2= (10)^2
                 => (8)^2+height^2= 100
                 => height^2= 100-(8)^2=100-64=36
               therefore height=  √36= 6cm.
Now, area of the isosceles triangle= 1/2*base*height
                                                       =1/2*16*6
                                                       =48 cm^2