Question

the perimeter of a right angle triangle is 40 cm . its hypotenus is 17cm . find the sides containing the right angle. also find the area of the triangle​

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 60cm²

Hope it's helpful