Question

heyy guys!!#NO SPAMS#

the side of a ri8-angled triangle containing the ri8-angle r 5x cm and (3x-1)cm.calculate the length of the hypotenuse of the triangle if its area is 60 cm ^2.


the 1st one 2 answer my question correctly will be marked as brainliest :) ^__^

Answer 1

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

Answer 2

first side =5x
second side =3x-1
area of triangle = 60 cm^2
area of triangle= 1/2 * b*h
60 =1/2*5x*(3x-1)
60*2= 5x(3x-1)
120 = 15x^2 -5x
15x^2 -5x -120 = 0
by dividing this by 5
3x^2 -x -24
D=b^2-4ac = (-1)^2 -4*3*-24
= 1 +288 = 289
x = -(b)+_√D
2a
= -(-1) +_√289
2*3
= 1 +_17 =1+17 or. =1-17
6 6 6
=18 =-16
6 6
=3 =-2.6
now as side can not be negative
so, let x = 3

by using Pythagoras Theorem
H^2 = P^2 + B^2
= (5x)^2 + (3x-1)^2. {(a-b)^2=a^2+b^2-2ab}
= 25x^2 + 9x^2 +1 -6x
=34x^2 -6x +1
now by putting value of x in H^2
H^2 = 34(3)^2 -6(3) +1
= 34*9 -18 +1
= 306 -17
= 289

H = √289
= 17
so hypotenuse = 17

I hope this helps u....