Answer:
|AC| = 132 cm (nearest centimetre)
Step-by-step explanation:
Pythagoras Theorem
Pythagoras Theorem explains the relationship between the three sides of a right triangle. The formula is:
[tex]\large\boxed{c^2=a^2+b^2}[/tex]
where:
- a and b are the legs of the right triangle
- c is the hypotenuse (longest side) of the right triangle.
From inspection of the given right triangle:
- a = AB = 45 cm
- b = BC = 124 cm
- c = AC
Substitute the given values into the formula and solve for AC:
[tex]\begin{aligned}c^2 & = a^2+b^2 &\\\\\implies AC^2&=AB^2+BC^2\\ AC^2&=45^2+124^2\\ AC^2&=2025+15376 \\ AC^2&=17401\\\sqrt{ AC^2}&=\sqrt{ 17401}\\ AC&=131.91285\\AC&=132\; \sf cm \; (nearest\;centimetre)\end{aligned}[/tex]
Therefore, |AC| is 132 cm to the nearest centimetre.
