Question

the sum of two smaller sides of a right angled triangle is 17 cm and the perimeter is 30cm, then find the area of the triangle.

Answer 1

hypotenuse =30-17=13
${a}^{2} + {b}^{2} = {c}^{2}$
Pythagoreas theorem
${(a + b)}^{2} - 2ab = {c}^{2}$
a+b=17
${17 }^{2} = 289$
${13}^{2} = 169$
289-2ab=169
2ab=289-169
2ab=60
ab=30
area=1/2×ab
=1/2×60{from above}
=30


Possibly 12 and 5 can be the sides as all of the three form pythagorean triplet and 12+5=17
now area =1/2×12×5=30