Question

The sides of a right angled triangle containing the right angle are 5x CM and (3x-1)cm calculate the length of its hypotenuse of the triangle if it's area is 60 CM square

Answer 1

Heya !!





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.

Answer 2

Answer:

hypotenuse=17 cm

Step-by-step explanation:

Height=5x cm

Base=(3x-1) cm

Area of triangle=1/2(b*h)

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

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

​120=15x^2-5x

15x^2-5x-120=0

Dividing both sides by 5,

3x^2-x-24=0

3x^2-9x+8x-24=0

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

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

x=3,x=-8/3

Since length cannot be -ve,so x=3.

Height=5x=15 cm , Base=3x-1=8 cm

By pythagoras theorem,

                         =(8)^2+(15)^2

                         =64+225

                         =289

hypotenuse=17 cm