Question

𝐴𝐵𝐶 is a triangle, right-angled at 𝐶. If 𝐴𝐵 = 25 𝑐𝑚 and 𝐴𝐶 = 7 𝑐𝑚, find 𝐵𝐶.

Answer 1

In ∆𝐴𝐵𝐶

Hypotenuse = AB = 25 cm

Base = AC = 7 cm

Perpendicular = BC = ?

Using Pythagoras theorem for the triangle,

$Hypotenus{e}^2$ = $Perpendicula{r}^2$ + $Bas{e}^2$

We can write,

$Perpendicula{r}^2$ = $Hypotenus{e}^2$ - $Bas{e}^2$

$B{C}^2$ = $A{B}^2$ - $A{C}^2$

= ${25}^2$+ $7^2$

= 625 + 49

= 576

Hence, BC = $\sqrt{576}$

= 24 cm

So the length of BC is equal to 24 cm.