Question

ABC is
a
triangle right angled
If AB = 25cm and
and AC= 7cm
find BC.
1​

Answer 1

Answer:

Step-by-step explanation:

Correct Question:-

ABC is a triangle, right angled at C. If AC = 7 cm AB = 25 cm find AB.

$\setlength{\unitlength}{1cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(.3,2.5){\large\bf 7}\put(2.8,.3){\large\bf ?}\put(1.02,1.02){\framebox(0.3,0.3)}\put(.7,4.8){\large\bf A}\put(.8,.3){\large\bf C}\put(5.8,.3){\large\bf B}\qbezier(4.5,1)(4.3,1.25)(4.6,1.7)\put(3.8,1.3){\large\bf }\end{picture}$

Answer:-

We need to find out the value of Height.

Concept:-

Pythagoras Theorem

Let's Do!

We know that the Pythagoras theorem states that the sum of the square of base and height of a right angle triangle is equal to square of its hypotenuse.

$\sf{AC^2+CB^2=AB^2}$

$\sf{7^2+CB^2 = 25^2}$

$\sf{BC^2 = 625-49}$

$\sf{BC = 24 \ cm}$

Note:-

• The question was completely dependant on the Pythagoras Theorem.
• hence, we should keep an eye on Prime factorisation and calculations also.
• Refer attachment if figure not visible.

Answer 2

✏CORRECT QUESTION

ABC is a triangle, right angled at C. If AC = 7 cm AB = 25 cm find AB.

✏SOLUTION

In ∆ABC, right angled at C,

AB = 24 cm, AC = 7 cm, BC =?

✒By Pythagoras theorem,

AB²= AC ²+ BC²

(25)²= (7)²+ BC²

625 = 49 + BC²

625 - 49 = BC ²

576 = BC ²

✒By taking prime factorization

2|576

2|288

2|144

2|72

2|36

2|18

3|9

3|3

| 1

576 = 2 x 2 x 2 x 2 x2 x 2 x 3 x 3

= (2 x 2 x 2 x 3) x (2 x 2 x 2 x 3)

= 24 x 24

24²

24²= BC²

✒Cancelling squares

24 = BC

BC = 24

BC = 24 cm

Hence Verified ☑

(Refer to the Attachment)