Question

if the the perimeter of a right triangle is 60 cm anf
its hypotenuse is 25 cm find the area of the triangle

Answer 1

perimeter =60

Alt+Bs+hypo =60

A+B+25=60

A+B=60-25

A+B=35

and by Pythagorean th

A^2+B^2= h^2 =25*25=625

from above we have
A+B =35

or

(A+B)^2= A^2+B^2+2AB

35*35 = 25*25 +2AB

35&35-25*25 =2AB

(35+25)(35-25)=2AB

60*10 =2AB

60*10/2=AB

300 =AB

NOW AREA OF right ∆ =1/2*base*altitude=1/2×A*B

=1/2*300

=150 sqcm

Answer 2

Perimeter of a right angled triangle = 60 cm

Let it's hypotenuse be 'h' and other two sides are 'a' and 'b'

We have,

=> a + b + h = 60 cm

and, h = 25 cm

So, a + b = 60 cm - 25 cm

=> a + b = 35 cm

Now, as per Pythagoras Theorem :-

=> a² + b² = h²

=> a² + b² = (25)²

=> a² + b² = 625

=> (a + b)² - 2ab = 625

=> (35)² - 2ab = 625

=> 1225 - 2ab = 625

=> -2ab = 625 - 1225

=> ab = (1225 - 625)/2

=> ab = 300 cm²

Thus, area of this right triangle = ½ × a × b

= ½ × 300 cm²

= 150 cm²

Hope this helps......