Question

answer the following question with explanation please give me a correct answer please don't give a fake answers if you give me a correct answer so I mark as brinialist.​

Answer 1

Answer:

x = 3

Area = 6

Step-by-step explanation:

Since the  longest side is 5, it must be the hypotenuse of the triangle. And the remaining side( x and x + 1 ) must be the legs.

  Using Pythagoras theorem:

⇒ 1st leg^2 + 2nd leg^2 = hypo^2

⇒ x^2 + ( x + 1 )^2 = 5^2

⇒ x^2 + x^2 + 1^2 + 2(x*1) = 25

⇒ 2x^2 + 1 + 2x = 25

⇒ 2x^2 + 2x + 1 - 25 = 0

⇒ 2x^2 + 2x - 24 = 0

⇒ x^2 + x - 12 = 0

⇒ x^2 + 4x - 3x - 12 = 0

⇒ x( x + 4 ) - 3( x + 4 ) = 0

⇒ ( x + 4 )( x - 3 ) = 0

⇒ x = 3 { x ≠ -ve }

  Hence,

x = 3 and other side = x + 1 = 3 + 1 = 4

 Area of tri. = 1/2 of product of sides

         = 1/2 * 3 * 4

         = 6

Answer 2

$\mathcal{\huge{\underline{\underline{\red{Question}}}}}$

✒ The three sides of a right-angled triangle are x, x+1 and 5. write down the value of x and the area, if the longest side is 5.

$\mathcal{\huge{\underline{\underline{\green{Answer:-}}}}}$

➡ Option D. ( 3 , 6 )

$\mathcal{\huge{\underline{\underline{\orange{Solution:-}}}}}$

Given :-

The three sides of a right-angled triangle are x, x+1 and 5. The area, if the longest side is 5

To Find :-

The value of x

Calculation :-

According to the question, By pythagoreas theorem,

(x + 1)² + x² = 5²

opening

(x + 1)² = x² + 1 + 2x

therefore

x² + 1 + 2x + x²= 25

2 x² + 2x = 24

2( x² + x) = 24

x² + x = 12

x² + x - 12 = 0

x²+ 4x - 3x - 12 = 0

x(x + 4) - 3(x + 4) = 0

(x - 3)(x + 4) = 0

either x=3 or x=-4

but side cannot be negative therefore x=3

hence, other side = - 4

Area=1/2×4×3

=2×3

=6 cm²

Hence, area = 6sq cm

✒ (3,6)

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