Question

Help with 21 would be much appreciated.

Answer 1

`\large\boxed{x=2√(21)\ and\ y=4\sqrt3}`

Explanation:

Look at the picture.

ΔADC and ΔCDB are similar. Therefore the sides are in proportion:

`(AD)/(CD)=(CD)/(DB)`

We have

`AD=14-8=6\\CD=y\\DB=8`

Substitute:

`(6)/(y)=(y)/(8)` cross multiply

`y^2=(6)(8)`

`y^2=48\to y=√(48)\\\\y=√(16\cdot3)\\\\y=√(16)\ cdot\sqrt3\\\\\boxed{y=4\sqrt3}`

For x use the Pythagorean theorem:

`x^2=6^2+(4\sqrt3)^2\\\\x^2=36+48\\\\x^2=84\to x=√(84)\\\\x=√(4\cdot21)\\\\x=\sqrt4\cdot√(21)\\\\\boxed{x=2√(21)}`