Math, asked by kt61430, 10 months ago

The sides of a right truangle containing the right angle are 5x and 3x-1 if the area of the triangle is 60cm^2 ,find the sides of triangle

Answers

Answered by anonymous0615105
4

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!

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Answered by mhanifa
0

Answer:

8 cm, 15 cm, 17 cm

Step-by-step explanation:

Area of right triangle = ab/2, where a and b are sides adjacent to right angle.

Here we have: a= 5x, b=3x-1, area=60 cm^2

Considering given in the formula we get:

5x*(3x-1)/2=60

3x^2-x=24

3x^2-x-24=0

Integer solution of this quadratic equation is x=3

So sides of the triangle: a=15 cm, b=8 cm

Hypotenuse of the triangle = sqrt(15^2+8^2)=17 cm

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