Question

If a right angle triangle has area and perimeter 40,40 ie same then find it's hypotynuse

Answer 1

Answer:

In a Triangle ABC of length a,b and c where is a hypotenuse

According to the question

Perimeter of a Triangle is 40cm i.e.,

a+b+c = 40

a +b = 40-c …….. eq. 1

and we know that from PGT

a^2 + b^2 = C^2 ……….eq. 2

and also 1/2(ab) = 40

ab = 80 … eq.3

now squaring on both side eq.1

( a + b )^2 = (40-C)^2

a^2 + b^2 + 2ab = 1600 -80c+c^2

c^2 + 2(80) = 1600 - 80c + c^2 (from eq.2 and eq.3 a^2+ b^2 = c^2 and ab = 80)

now by solving this you will get

c = 18 cm , so the length of hypotenuse is 18cm