Question

let a and b be a length of legs and let c be hypotenuse of a right angle triangle then pt (1+c/a)(1+c/b)>=3+2√2​

Answer 1

Step-by-step explanation:

a right triangle has sides labeled a, b, and c where c is the hypotenuse

if it's also an isoscelese triangle, then a=b

the pythagorean theorem is c^2 = a^2 + b^2, which for an isosceles becomes c^2=a^2+a^2 = 2a^2

If area = c^2/4 = ab/2 = a^2/2

then c^2=2a^2 and

c =asqr2

the triangle has hypotenuse = sqr2 times a or b

It's a triangle with angles C=90 degrees, A=B=45 degrees

by law of sines

sinA/a = sinB/b = sinC/c

sin45=1/sqr2

sin90 = 1

1/sqr2/a = 1/sqr2/b = 1/c = 1/asqr2

1/sqr2/a= 1/sqr2 x 1/a = 1/asqr2

a is the side opposite angle A

b is the side opposite angle B

c is the side opposite angle C

You know everything about the triangle except how big it is

You know all 3 angles, plus the ratio of the 2 equal sides to the hypotenuse

Once you know it's a 45-45 -90 right triangle you also know 2 sides are equal & it's an isosceles triangle.