Question

In the right triangle ABC altitude bd is drawn to hypotenuse AC . If AD equals 8 and DC equals 10 determine the length of AB

Answer 1

step 1

In the right triangle BDC

Applying Pythagorean Theorem

BC^2=BD^2+DC^2

substitute given value

BC^2=BD^2+10^2 -----> equation 1

step 2

In the right triangle ABD

Applying Pythagorean Theorem

AB^2=BD^2+AD^2

AB^2=BD^2+8^2

AB^2=BD^2+64 -----> equation 2

step 3

In the right triangle ABC

AC^2=AB^2+BC^2

18^2=AB^2+BC^2 ------> equation 3

substitute equation 1 and equation 2 in equation 3

so

18^2=(BD^2+64)+(BD^2+100)

solve for BD

324=2BD^2+164

2BD^2=324-164

2BD^2=160

BD^2=80

Find the value of AB

Remember equation 2

AB^2=BD^2+64

substitute

AB^2=80+64

AB^2=144

therefore

AB=12 units