Question

In triangle ABC AB is equal to 26 CM BC is equal to 28 cm and the altitude ad is equal to 24 cm calculate AC

Answer 1

$\textbf{\huge{ANSWER}}$

$<marquee>✌️REFER TO THE ATTACHMENT ✌️$

Answer 2

Thus, The value of $AC$ is $30cm$

Step-by-step explanation:

Given,

In $\triangle ABC$, $AB=26cm$ , $BC=28cm$ and altitude $AD=24cm$

From figure,

In $\triangle ABD$,

$BD^{2} =AB^{2} -AD^{2}$

⇒$BD=\sqrt{26^{2} -24^{2}}$

⇒$BD=\sqrt{100}$

⇒$BD=10$

∴$DC=BC-BD=28-10=18$

In $\triangle ADC$,

$AC^{2} =AD^{2} +DC^{2}$

⇒$AC=\sqrt{24^{2} +18^{2} }$

⇒$AC=\sqrt{576+324}$

⇒$AC=\sqrt{900}$

∴$AC=30$

So, The value of $AC$ is $30cm$