Find the exact value of y

Question

asked Sep 6, 2019 104k views

1 Answer

David Lilljegren · Answer 1 · 2019-09-09T21:05:47+0000

Look at the picture.

Use the Pythagorean theorem to solve h:

h^2+5^2=7^2

h^2+25=49 subtract 25 from both sides

$h^2=24\to h=√(24)$

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

(h)/(5)=(x)/(h) cross multiply

5x=h^2 put the value of h

5x=(√(24))^2

5x=24 divide both sides by 5

x=4.8

y = 5 + x → y = 5 + 4.8 = 9.8

Or other method. ΔADC and ΔACB are similar. Therefore the sides are in proportion:

(y)/(7)=(7)/(5) multiply both sides by 7

$y=(49)/(5)\\\\\boxed{y=9.8}$