Question

the perimeter of a right angle triangle is 40 cm if its hypotenuse is 17 cm find the area ...

please help Mee...​

Answer 1

Answer:

The perimeter of a right triangle =40cm

Hypotenuse measures =17cm.

Let x and y are the another sides.

40=17+x+y

x+y=23

or y=23−x

So, we have 3 sides as x,23−x and 17.

Apply Pythagoras theorem:

Hypotenuse

2

= Base

2

+ Perpendicular

2

17

2

=x

2

+(23−x)

2

289=x

2

+529+x

2

−46x

x

2

−23x+120=0

(x−8)(x−15)=0

x=8 or x=15

If x=8 then y=23−8=15

If x=15 then y=23−15=8

Now,

Area of triangle =

2

1

×base×height

=

2

1

×8×15

=60

Therefore, Area of triangle is 60cm

2

Answer 2

Step-by-step explanation:

let x &y be another sides

40=17+x+y

23=x+y

y=23-x

now three sides are x, 23-x,17

by pythogoras theorem

hypotenuse ^2 =base^2+perpendicular side^2

17^2=x^2+23-x^2

289=x^2+529-46x+x^2

x^2-23x+120=0

(x-15) (x-8)

x=15 or x=8

y= 23-15

y=8

if we had chossen x =8

y =23-8

y =15

area of triangle = 1/2 × base ×height

= 1/2 ×8×15

=60cm^2