Question

ABC is a triangle, right-angled at C. If AB = 15 cm and AC = 12 cm, then BC = ____ *
1 point
9 cm
27 cm
81 cm
3 cm

Answer 1

The base of right triangle

The right angled triangle has three sides and that is, hypotenuse, perpendicular and base respectively.

Here in this question we've been given that, there's a right angled triangle named ABC, where the value of AB is 15 cm and the value of AC is 12 cm.

With this information, we've been asked to find out the value of BC.

So, the diagram for this question would be like this:

$\setlength{\unitlength}{1.9cm}\begin{picture}(6,2)\linethickness{0.5mm}\put(7.7,2.9){\large\sf{A}}\put(7.7,1){\large\sf{C}}\put(10.6,1){\large\sf{B}}\put(8,1){\line(1,0){2.5}}\put(8,1){\line(0,2){1.9}}\qbezier(10.5,1)(10,1.4)(8,2.9)\put(8.6,0.7){\sf{\large{? cm}}}\put(8.2,1){\line(0,1){0.2}}\put(8,1.2){\line(3,0){0.2}}\put(7.4,1.8){\sf 12 cm}\put(9.4,2.2){\sf 15 cm}\end{picture}$

[Kindly check the attachment for the diagram, if the diagram is not visible on app]

Since the traingle is in right angled, we know that if the triangle is in right angled then we generally use Pythagoras theorem to find any value in right angled triangle.

We know that, In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

In mathematical term the pythagoras theorem will be,

$\implies (AB)^2 = (AC)^2 + (BC)^2$

Here AB is the Hypotenuse, AC is the Perpendicular and BC is the base of right angled triangle respectively.

So here we can conclude that we need to calculate the base of a right angled triangle.

Now by using the pythagoras theorem and substituting all the available values in the formula, we get:

$\implies (15)^2 = (12)^2 + (BC)^2 \\ \\ \implies 225 = (12)^2 + (BC)^2 \\ \\ \implies 225 = 144 + (BC)^2 \\ \\ \implies (BC)^2 = 225 - 144 \\ \\ \implies (BC)^2 = 81 \\ \\ \implies BC = \sqrt{81} \\ \\ \implies \boxed{BC = 9}$

Therefore, the value of BC is 9cm. So, option (a) is the correct option for this question.

Answer 2

Given :-

ABC is a triangle, right-angled at C. If AB = 15 cm and AC = 12 cm

To Find :-

Length of BC

Solution :-

We know that

H² = P² + B²

Here

H = AB = 15 cm

P = AC = 12 cm

B = BC = ?

Let the length of BC be a

(AB)² = (AC)² - (BC)²

(AB)² - (AC)² = BC²

(15)² - (12)² = BC²

225 - 144 = BC²

81 = BC²

√(81) = BC

9 = BC

Therefore

Option A is correct