Question

The lenght of the sides forming right angled triangle are 5x and (3x-1)cm .if the area the area of the triangle triangle is60 find its hypotenuse...

Answer 1

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 cm
and, 3x - 1 = (3 × 3) -1
⇒ 9 - 1 = 8 cm.
According to Pythagoras Theorem,
Hypotenuse² = Base² + Perpendicular²
H² = (8)² + (15)²
H² = 64 + 225
H² = 289
H = √289
Hypotenuse = 17 cm
answer.

Answer 2

$\huge\underline{ \underline{ \red{answer = {17cm}^{2} }}}$

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 cm

and, 3x - 1 = (3 × 3) -1

⇒ 9 - 1 = 8 cm.

According to Pythagoras Theorem,

Hypotenuse² = Base² + Perpendicular²

H² = (8)² + (15)²

H² = 64 + 225

H² = 289

H = √289

H=17

$\huge{ { \red{ {h = 17cm}^{2} }}}$