Question

Q. 5

In right angled ∆ABC ,
AB = ( x + 1 ) cm

BC = x cm

AC = ( x + 2 ) cm

Find the area of ∆ABC

CBSE | Class 10 |

Answer 1

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Answer 2

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GIVEN that:-

∆ABC is 90°

AB = ( x + 1 ) cm

BC = x cm

AC = ( x + 2 ) cm



Now use Pythagoras theorem,

AC² = AB² + BC²

=> (x + 2)² = x² + (x + 1)²

=> x² + 4 + 4x = x² + x² + 1 + 2x

=> 2x² - x² + 2x - 4x + 1 - 4 = 0

=> x² - 2x - 3 = 0

=> x² - 3x + x - 3 = 0

=> x(x - 3) + 1(x - 3)

=> (x + 1)(x - 3)

=> x = -1 , x = 3


Now,

AB = (x + 1) = (3 + 1) = 4cm

BC = x = 3cm

AC = (x + 2) = (3 + 2) = 5cm



We know that:-

IN righ triangle area = 1/2 × AB × BC

=> 1/2 × 4 × 3

=> 2 × 3

=> 6cm²



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