What is the value of y?

17.5 ft
12.5 ft
11.6 ft
16.5 ft

(Image is attached)

y = 16.5

Step-by-step explanation:

We would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Considering triangle BCD,

BD² = 14² - 8²

BD² ° 196 - 64 = 132

BD = √132

Considering triangle ABD,

AB² = BD² + y²

AB² = (√132)² + y²

AB² = 132 + y²- - - - - - - - - - 1

Considering triangle ABC,

(8 + y)² = AB² + BC²

(8 + y)² = AB² + 14²

(8 + y)² = AB² + 196

AB² = (8 + y)² - 196- - - - - - - -2

Substituting equation 1 into equation 2, it becomes

132 + y² = (8 + y)² - 196

y² - (8 + y)² = - 196 - 132

y² - (64 + 16y + y²) = - 328

y² - 64 - 16y - y2 = - 328

- 16y = - 328 + 64

- 16y = - 264

y = - 264/- 16

y = 16.5

the answer is here: : )

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