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

Answer:

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

$BD^2 +DC^2 = BC^2$

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:

$AB = \sqrt{72}=8.48528137$ cm

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