This has to be determined by pythagorian theorem. Hence the value of AB= 4 units and BD= 2.4 units.
Given: AD = 3.2 units
BC = 3 units
CD = 1.8 units
Find : AB =? units
BD=? units
As we know that ,
By the formula of pythagorian theorem,
Let be a ΔABC,
[tex]\bold{(AB)^{2} = (BC)^{2} +(AC)^{2}}[/tex]
From the above formula now determined the value of AB and BD,
Firstly , find the value of BD
In ΔBDC, by applying pythagaorian theorem,
[tex]\bold{(BC)^{2} = (BD)^{2} +(DC)^{2}}[/tex] ...(1)
Here, BC = 3 units and CD = 1.8 units
Now put the values of BC and CD in (1),
[tex]\begin{aligned}(3)^{2} &=(BD)^{2}+(1.8)^{2}\\9&=(BD)^{2}+3.24\\9-3.24&=(BD)^{2}\\5.76&=(BD)^{2}\\\sqrt{5.76} &=BD\\\bold{BD&= 2.4}\:units\end{aligned}[/tex] ...(2)
Now find the value of AB,
In ΔABD, by applying pythagorian theorem,
[tex]\bold{(AB)^{2}=(AD)^{2} + (BD)^{2} }[/tex] ...(3)
Here, AD=3.2 and from (2) BD=2.4
By putting values in (3) ,
[tex]\begin{aligned}(3.2)^{2} +(2.4)^{2}&=(AB)^{2}\\10.24+5.76&=(AB)^{2}\\16&=(AB)^{2}\\\sqrt{16} &=AB\\\bold{AB&= 4}\:units\end{aligned}[/tex]
Therefore,the values of AB=4 units and BD= 2.4 units.
For further details, please prefer this link:
https://brainly.com/question/343682
