Question

Please solve this question.

Answer 1

sides of a right-angled triangle are 5x and (3x - 1)cm. 

Area of the triangle = 60cm^2. 

We know that Area of the triangle = 1/2 * b * h 
                                                  60 = 1/2 * 5x * (3x - 1) 
                                      5x(3x - 1) = 60 * 2 
                                      5x(3x - 1) = 120 
                                        x(3x - 1) = 120/5 
                                         3x^2 - x = 24 
                                  3x^2 - x - 24 = 0 
                        3x^2 + 8x - 9x - 24 = 0 

                              x(3x + 8) - 3(3x + 8) 
                              (x - 3)(3x + 8) 
                              x = 3 (or) x = -3/8. 
x value should not be -ve.Therefore the value of x = 3. 

∴sides of a right-angled triangle =  5x = 5 * 3 = 15cm 
                                       (3x - 1) = (3 * 3 - 1)= 9 - 1 = 8cm 
  
By Pythagoras theorem, we know that  
h^2 = 15^2 + 8^2 
       = 225 + 64 = 289 
        h =17. 
Therefore the hypotenuse = 17cm. 
Therefore the sides of the triangle are 8cm,15cm, and 17cm.

Answer 2

Step-by-step explanation:

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5X and 3X - 1 are the two side of the right angled triangle.

Area of triangle = 60

1/2 × 5X × ( 3X - 1 ) = 60

5X ( 3X - 1 ) = 120

15X² - 5X - 120 = 0

5 ( 3X² - X - 24 ) = 0

3X² - X - 24 = 0

3X² - 9X + 8X - 24 = 0

3X ( X - 3 ) + 8 ( X - 3 ) = 0

( X - 3 ) ( 3X + 8 ) = 0

( X - 3 ) = 0

X = 3

Hence,

its two given Sides are 15 cm and 8cm .

By Pythagoras theorem ,

Hypotenuse² = (15)² + (8)²

Hypotenuse² = 289

Hypotenuse = root 289 = 17 cm.