Question

Find the value of y.

A.
$\sqrt{55}$
B. 6
C.
$8 \sqrt{3}$
D.16​

Answer 1

Answer:

$y=\sqrt{55}$

which agrees with answer A

Step-by-step explanation:

Notice there are three right angle triangles for which we can apply the Pythagorean theorem:

In the small triangle at the bottom we have the Pythagorean theorem rendering:

(a)

$5^2+y^2=x^2\\x^2=25+y^2$

in the second right angle triangle on top of the previous one, if we call the vertical side on the right side "z", we have:

(b)

$11^2+y^2=z^2\\z^2=121+y^2$

and finally in the large right angle triangle:

(c)

$z^2+x^2=16^2\\z^2=256-x^2$

We can combine equations b and c to obtain:

$121+y^2=256-x^2\\x^2+y^2=256-121=135\\x^2=135-y^2$

and then combine this and (a) to get:

$25+y^2=135-y^2\\2\,y^2=135-25\\2y^2=110\\y^2=55\\y=\sqrt{55}$