Question

In the given figure, angle 𝐴𝐷𝐵 = 90°, 𝐴𝐶 = 𝐴𝐵 = 26 𝑐𝑚 and 𝐵𝐷 = 𝐷𝐶. If the length of 𝐴𝐷 = 24 𝑐𝑚; find the length of 𝐵𝐶.

Answer 1

Step: Applying Pythagoras theorem to find length of base

𝑆𝑖𝑛𝑐𝑒, ∆ADB is a right- angled triangle with vertex D,

According to Pythagoras theorem,

$(Hypotenuse{)}^2$ = $(Perpendicular{)}^2$ + $(Base{)}^2$

$(AB{)}^2$ = $(AD{)}^2$ + $(BD{)}^2$

$(26{)}^2$ = $(24{)}^2$ + $(BD{)}^2$

676 = 576 + $(BD{)}^2$

$(BD{)}^2$ = 676 - 576

=100

BD = $\sqrt{100}$

= 10 cm

∵ length of BC = BD + DC

BC = 10 + 10 (Given DC=BD)

BC = 20 cm

Hence, BC = 20 cm.