Question

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Answer 1

Answer:

Your answer is option ( b ) 6 $cm^2$

Step-by-step explanation:

In right-angled triangle ABC,

$(x + 2)^2 = x^2 + ( x + 1 )^2$   ...................( By pythagoras theorem)

⇒$x^2 + 4 + 4x = x^2+x^2+1+2x$

⇒$x^2-2x-3 = 0$    

By using quadratic formula,

$x=-b±\sqrt{b^2-4ac} / 2a$ .......................( 1 )

Here , a = 1

          b = -2

          c = -3

Substituting the values of a, b and c in ( 1 ),

$x = -(-2)± \sqrt{(-2)^2 - 4*1*(-3) } / 2 * 1$

⇒ x = 2 ± $\sqrt{4 - (- 12)} / 2$

⇒ x = 2 ± $\sqrt{4+12} / 2$

⇒ x = 2 ± $\sqrt{}$16 / 2

⇒ x = 2 ± 4 /2

⇒ x = 2 + 4 / 2 , 2 - 4 / 2

⇒ x = 6 / 2 , -2 / 2

⇒ x = 3 , -1

But, x cannot be negative.

⇒ x = 3

∴ AB = 3 cm, BC = 4cm , CA = 5 cm

Area of triangle = 1 / 2 * AB *BC

                          = 1 / 2 * 3 * 4

                          = 12 / 2

                          = 6 $cm^2$ ( b )

HOPE IT HELPS.......................

Plz mark this answer as brainliest ..........