The diagram Shows a right-angled triangle abc in which ab =12 cm and Ac=15 cm
Show that the length of bc is 9 cm
let abc a triangle ac=15 (hypot) (ac)2= (ab)2 + (bc)2
(15)2 = (12)2 + (bc)2
bc = 9
To show that the length of bc is 9 cm, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, side ab is one of the legs of the triangle, and side ac is the hypotenuse.
Let's denote the length of bc as x.
According to the Pythagorean theorem, we have:
ab^2 + bc^2 = ac^2
Substituting the given values, we have:
12^2 + x^2 = 15^2
Simplifying, we get:
144 + x^2 = 225
Now, let's solve for x:
x^2 = 225 - 144
x^2 = 81
Taking the square root of both sides, we have:
x = √81
x = 9
Therefore, the length of bc is indeed 9 cm.