Question

The lengths of the sides forming right angle triangle are 5x and (3x – 1) cm. If the area of the triangle is 60
sq.cm, find its hypotenuse?

Answer 1

Answer:

1/2 bh 

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

1/2 (15x^2 -5x ) = 60

15x^2 - 5x = 120

15x^2 -5x - 120 = 0

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 = -8/3

since length cannot be -ve 

x = 3

so the sides of the triangle are 

5(3) and 3(3) - 1 = 15 and 8 

By Pythogorean prop 

8^2 + 15^2 = hypotenuse ^2 

(sum of the squares on the two non - hypotenuse sides is equal to the square on the hypotenuse )

64 + 225 = 289 

hypotenuse sqr = 289

hypotenuse = Root of 289

Hyp - 17

Answer 2

Step-by-step explanation:

Given.

5x cm and (3x-1) cm are the two sides of a right triangle.Area of the triangle = 1/2 × Base × Height

=> 60 = 1/2 {5x (3x-1)}

=> 60 = 1/2(15x² - 5x)

=>120 = 15x² - 5x 

=>Dividing both sides by 5, we get

=>24 = 3x² - x

=> 3x² - x -24 = 0

=>3x² + 8x - 9x - 24

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

=> (x - 3) (3x + 8)

=> x - 3 = 0

=> x = 3

=>3x + 8 = 0

=>3x = -8

=> x = - 3/8

since ,

the length cannot be negative so,

x = 3 is the correct value.Therefore, the sides of the triangle are,5x = 5 × 3 = 15 cmand, 3x - 1 = (3 × 3) -1

= >9 - 1 = 8 cm.

9 - 1 = 8 cm

Theorem,Hypotenuse² = Base² + Perpendicular²

H² = (8)² + (15)²

H² = 64 + 225

H² = 289

H = √289

Hypotenuse = 17 cm