Question

AABC and AXYZ are equilateral triangles. BC = 4 cm. XY = 12 cm.
then A (AABC): A(AXYZ) =
a) 4:9
b) 1:9
c) 2:3
d) 1:8​

Answer 1

Answer:

side of tri abc , bc=4

height of tri abc , h1=√bc^2-(1/2*bc)^2

h1 =√16-4=√12

h1=2√3

area of tri abc = 1/2 * bc * h1

=1/2*4*2√3

=4√3

side of tri xyz , xy= 12

height of tri xyz, h2=√xy^2-(1/2*xy)^2

h2=√144-36=√108

h2=√3*4*9=6√3

h2=6√3

area of tri xyz =1/2 * xy * h2

=1/2*12*6√3

=36√3

so area of tri abc: area of tri xyz= 4√3:36√3

=1:9