Given: ac is the hypotenuse and bd is the altitude of △abc. ad=27, cd=40, ab=e, bd=j, and bc=h
find the value of e
how the literal devil am i supposed to do this, legit i've tried for hours first answer gets brainliest

Check the picture.

In triangle ABC:

m(B)=90°, let m(A)=α, and let m(C)=β

so m(B)+m(A)+m(C)=180°, so α+β=90°

In triangle ABD, m(A)=α, m(ADB)=90° so m(ABD) must be β, so that the sum completes to 180.

By the same logic, m(DBC)=α

so we have the following similarities of triangles: (let's go by the order α-β-90°):

ACB ≡ ABD ≡ BCD, 

consider ABD ≡ BCD:



substitute with the givens:



from 



we have 



In triangle ABD, from the pythagorean theorem:



so 

Remark: a direct solution can be given by Euclid's theorem, AB^2=AD*AC

so 

 , then take square root of e

42.53 units

There should only be 1 solution