Question

Consider the right triangle ABC given below: The altitude divides triangle ABC into two smaller right triangles, and all three triangles are 45-45-90 triangles

i. What is the length of the BC (x in the picture)?

ii. What is the length of CD (y in the picture)?

iii. What is the length of BD (z in the picture)?

Please Show Your Work

Answer 1

x =8

y = 4sqrt(2)

z = 4sqrt(2)

Explanation:

The easiest one to calculate is x

If it is a 45 -45-90 degree triangle then AB = BC=x

Since AB =8 then BC =8 and x=8

The next easiest to calculate is z

If it is a 45 -45-90 degree triangle then AD = BD=z

Using the Pythagorean theorem

z^2 +z^2 = 8^2

2z^2 =64

Divide by 2

x^2 = 32

Taking the square root of each side

z = sqrt(16)sqrt(2)

z=4sqrt(2)

Finally, we can find y

If it is a 45 -45-90 degree triangle then BD = DC

BD =z =4 sqrt(2) = DC = y

Therefore y =4 sqrt(2)