Question

Find the values of X and y
​

Answer 1

x =
`17(1)/(7)`

y =
`8(4)/(7)`

Explanation:

1. Lines DE and AC are parallel.

Therefore, by the Triangle Proportionality Theorem:

`(SideBD)/(SideAD) = (SideBE)/(SideEC)`
=
`(30)/(x) = (15)/(y)`

Rearranging:

`(30)/(15) = (x)/(y)`

`2 = (x)/(y)`

Cross-multiplication is applied:

`(x)(1) = (2)(y)`

`x = 2y` —-(equation i)

2. ΔBDE and ΔBAC are similar triangles

Which means:

`(SideBD)/(SideDE) = (SideBA)/(SideAC)`

`(30)/(14) = (30 + x)/(22)`

Cross-multiplication is applied

`(14)(30 + x) = (30)(22)`

`420 + 14x= 660`

`14x = 660 - 420`

`14x = 240`

`x = (240)/(14)`

Reduce the numerator and denominator by the Highest Common Factor (2):

∴x =
`(120)/(7)`

=
`17(1)/(7)`

Substitute the value of x in (equation i) to solve for y:

`(120)/(7) = 2y`

`y = (120)/(7(2))`

∴y =
`(60)/(7)`

=
`8(4)/(7)`

Answer 2

x=17/1/7, y=8/4/7

Explanation:

x:

30/30+x=14/22

420+14x=660

14x+240

x=17/1/7

y:

14/22=15/15+y

210+14y=330

14y=120

y=8/4/7