Question

The perimeter of a right triangle is 90 cm and its area is 180 cm^2. What is its hypotenuse?​

Answer 1

a ,b, c be sides of Rt angled Triangle c being hypotenuse

perimeter = a+ b+ c =90 cm therefor c=90–a -b & a +b=90-c

area =1/2* ab =180 ; ab=360

by Pythagoras theorem =a^2+b^2 =c^2 =[90-a-b]^2

a^2+b^2=8100 +a^2+b^2 -180a+2ab-180b

8100 -180a+2ab-180b=0 ; 8100 -180[a +b] +2*360=0

8100–180[90-c]+720=0

8820= 180*90+180c

8820= 16200+180c

-7380 =180c

c=-41

Hypotenuse c=41cms

To find other sides a & b

a+ b+ c =90 so a+b+41=90 ; a+ b= 90–41 =49 ; a =49-b

ab =360 ; [49-b]*b =360 ; 49b-b^2 =360 ; b^2–49b+360=0

b^2 -40b-9b+360=0 ;b[b-40]-9[b-40]=0 ; [b-9][b-40] =0

so b=9 or b=40

a+b+c =90 ; a =90-b-c ; =90–9–41 =40cm

Hypotenuse c=41cms