Calculate the length of ab. round to the nearest hundredth. if possible, explain your answer ( very much appreciated but not needed ) because i don’t understand this subject and i’m just trying to learn.

the length of AB nearest to hundredth is 8.48 cm

Step-by-step explanation:

Pythagoras theorem states that the square of the hypotenuse side is equal to the sum of the other two sides.

Labelled the diagram as shown below.

In a right triangle BDC.

DC = 9 cm , BD = x units and BC = 12 units

then,

by Pythagoras theorem in triangle BDC

Substitute the given values we have;

Simplify:

Subtract 81 from both sides we get;

cm

Now, in triangle BDA:

AD = 3 cm and BD = x cm

Using Pythagoras theorem, to solve for AB

Substitute the given values we have;

         .....[1]

Substitute the value of in [1] we get;

or

Simplify:

cm

Therefore, the length of AB nearest to hundredth is 8.48 cm

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!

b