An equalateral triangle has the length of it's sides given as (y+3)cm, (2y-x)cm and (4x +3)cm.Find (a) the value of x and y (b)perimeter of the triangle (c) altitude of the triangle to the nearest whole number

Answer 1

all 3 sides are equal , so form equations using any two pairs.

y+3 = 2y-x ---> y = 3+x

y+3 = 4x+3 --> y = 4x

so 4x = 3+x
3x=3
x = 1

then y = 4(1) = 4

x=1 , y=4

each side is 7 , perimeter is 21
for the height, use Pythagoras
3.5^2 + h^2 = 7^2
h = √36.75 = appr. 6.06

or

sin60° = h/7
h = 7sin60 = 6.06

Answer 2

all 3 sides are equal , so form equations using any two pairs.

y+3 = 2y-x ---> y = 3+x

y+3 = 4x+3 --> y = 4x

so 4x = 3+x
3x=3
x = 1

then y = 4(1) = 4

x=1 , y=4

each side is 7 , perimeter is 21
for the height, use Pythagoras
3.5^2 + h^2 = 7^2
h = √36.75 = appr. 6.06

or

sin60° = h/7
h = 7sin60 = 6.06