Question
Mathematics Question on Square Roots of Decimals
In a right triangle ABC, ∠B = 90°.
- If AB = 6 cm, BC = 8 cm, find AC
- If AC = 13 cm, BC = 5 cm, find AB
Answer
(a) △ABC is right-angled at B.
Therefore, by applying Pythagoras theorem, we obtain
AC2=AB2+BC2
AC2=(6cm)2+(8cm)2
AC2=(36+64)cm2
=100 cm2
AC=(100)cm=(10×10)cm
AC=10cm
(b) △ABC is right-angled at B.
Therefore, by applying Pythagoras theorem, we obtain
AC2=AB2+BC2
(13cm)2=(AB)2+(5cm)2
AB2=(13cm)2−(5cm)2
=(169−25)cm2
= 144cm2
AB=(144)cm=(12×12)cm
AB=12cm