Question

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.

Answer 1

the length of AB nearest to hundredth is 8.48 cm

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

`BD^2 +DC^2 = BC^2`

Substitute the given values we have;

`x^2 + 9^2 = 12^2`

Simplify:

`x^2+81=144`

Subtract 81 from both sides we get;

`x^2 =63` cm

Now, in triangle BDA:

AD = 3 cm and BD = x cm

Using Pythagoras theorem, to solve for AB

`BD^2 +AD^2 = AB^2`

Substitute the given values we have;

`x^2+3^2=AB^2` .....[1]

Substitute the value of
`x^2 =63` in [1] we get;

`63+9=AB^2`

or

`AB^2= 72`

Simplify:

`AB = √(72)=8.48528137` cm

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