Question

Please solve this question

Answer 1

Answer:

8 cm, 15 cm and 17 cm

Step-by-step explanation:

Area of a triangle = 1/2 x base x height

Find the area in term of x:

Area = 1/2 (5x) (3x - 1)

Area = 1/2 (15x² - 5x)

Solve x:

Given that the area is 60 cm²

1/2 (15x² - 5x)  = 60

15x² - 5x  = 120

15x² - 5x  - 120 = 0

3x² - x - 24 = 0

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

x = 3 or x = - 8/3 (rejected since length cannot be negative)

Find the length of the two sides:

one side = 5x = 5(3) = 15 cm

other side = 3x - 1 = 3(3) - 1 = 8 cm

Find the length of the third side:

The triangle is a right angle triangle

a² + b² = c²

c² = 15² + 8²

c² = 289

c = √289

c = 17 cm

Answer: The length of the triangle are 8 cm, 15 cm and 17 cm

Answer 2

Hello bhai



ur answer ⤵⤵⤵⤵⤵⤵⤵⤵⤵⤵⤵




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

Given that 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.

Therefore the 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.

Hope this helps!


@AMAN17H