Question

Round to nearest tenth if needed

Find the measure of Y

Answer 1

`\large\boxed{y=3\sqrt5\approx6.7}`

Explanation:

ΔABC and ΔDAC are similar. Therefore the corresponding sides are in proportion:

`(AC)/(BC)=(DC)/(AC)`

We have

`AC=y\\BC=3+12=15\\DC=3`

Substitute:

`(y)/(15)=(3)/(y)` cross multiply

`y^2=(15)(3)\\\\y^2=45\to y=√(45)\\\\y=√(9\cdot5)\\\\y=\sqrt9\cdot\sqrt5\\\\y=3\sqrt5\\\\y\approx6.7`