Question

The perimeter of a right triangle is 50 cm and the hypotenuse is 18 cm. Find its area. ​

Answer 1

Answer:

Step-by-step explanation:

let a is base , b is height and c is hypotenus

according to question

a+b+c=50---------(1)

a^2+b^2=c^2-----(2)

now equation (1)

a+b+c=50

a+b=50-c

squaring both side

(a+b)^2=(50-c)^2

a^2+b^2+2ab=2500+c^2-100c

put (2)

c^2+2ab=2500+c^2-100c

2ab=2500-100c

but hypotenus (c)=18

so,

2ab=2500-1800=700---------(3)

because

area of triangle=1/2base x height

=1/2ab

from(3)

area of triangle=1/2 x (700/2)=175cm^2

Answer 2

Answer:

let a is base , b is height and c is hypotenus

according to question

a+b+c=50---------(1)

a^2+b^2=c^2-----(2)

now equation (1)

a+b+c=50

a+b=50-c

squaring both side

(a+b)^2=(50-c)^2

a^2+b^2+2ab=2500+c^2-100c

put (2)

c^2+2ab=2500+c^2-100c

2ab=2500-100c

but hypotenus (c)=18

so,

2ab=2500-1800=700---------(3)

because

area of triangle=1/2base x height

=1/2ab

from(3)

area of triangle=1/2 x (700/2)=175cm^2