Question

Geometry, please answer question ASAP

Answer 1

XY = 24

Explanation:

In similar triangles, the corresponding sides are in same ratio.

`(AC)/(XZ)=(AB)/(XY)\\\\(x+6)/(30)=(16)/(2x-4)`

Cross multiply,

(x + 6 )(2x-4) = 16*30

Use FOIL method

x*2x + x*(-4) + 6*2x + 6*(-4) = 480

2x² - 4x + 12x - 24 = 480 {Combine like terms}

2x² + 8x - 24 = 480

2x² + 8x - 24 - 480 = 0

2x² + 8x - 504 = 0

Divide the entire equation by 2

x² + 4x - 252 = 0

Sum = 4

Product = -252

Factors = 18 , -14 {18 +(-14) = 4 & 18*(-14) = -254 }

x² + 4x - 252 = 0

x² + 18x - 14x - 252 = 0 {Rewrite middle term}

x(x + 18) - 14(x + 18) = 0

(x + 18)(x - 14) = 0

x - 14 = 0 {Ignore x + 18 = 0 as measurement will not come in negative}

x = 14

XY = 2x - 4

= 2*14 -4

= 28 - 4

= 24