Question

find the value of x ​

Answer 1

Step-by-step explanation:

AC². = AB²+BC²

(x+2)². = (5)²+(x-3)²

x²+4+4x=25+x²+9-6x

x²+4+4x=x²-6x+34

x²-x²+4x+6x=34-4

10x. =30

x=30/10

x=3

value of x=3

Answer 2

★ Diagram

$\setlength{\unitlength}{1mm}\begin{picture}(0,0) \thicklines\put(0,0){\line(3,0){2.45cm}} \put(0,0){\line(0,3){2cm}} \put(0,19.6){\line(5,-4){2.4cm}} \put(7,-3){\bf x - 3} \put(15,10){\bf x + 2} \put(-4,7){\bf 5} \put(0.2,0.3){\circle*{0.9}}\put(-3,-3){B}\put(24.6,0.2){\circle*{0.9}}\put(24.6,-3){C}\put(0,19.8){\circle*{0.9}}\put(-2,21){A}\end{picture}$

★ Solution :-

Length of lines .

• Height = AB → 5
• Base = BC → x - 3
• Hypotenuse = AC → x + 2

To find

• x = ?

Now , by using Pythagoras theorem

(Hypotenuse)² = (Base)² + (Height)²

Similarly

AC² = AB² + BC²

Substituting the known values we have

→ (x + 2)² = (x - 3)² + 5²

Simplifying , using (a + b)² = a² + b² + 2ab & (a - b)² = a² + b² - 2ab.

→ x² + 4x + 4 = x² - 6x + 9 + 25

→ x² + 4x + 4 - (x² - 6x + 9) = 25

→ x² + 4x + 4 - x² + 6x - 9 = 25

→ 10x - 5 = 25

→ 10x = 25 + 5

→ 10x = 30

→ x = 30 ÷ 10

→ x = 3

Hence, x = 3