In the right triangle ABC with right angle at A , the inradius is 2cm. If the hypothenuse BC=10cm , determine the perimeter and the are of the given triangle.

( please don’t use angle properties or trig )

24cm

Step-by-step explanation:

Inradius = r

c = the hypothenuse

a & b = the other 2 sides of the triangle

Inradius formula: r = 1/2 * (a+b-c)

Plug in what we know.

2 = 1/2 * (a+b-10)

Multiply both sides by 2.

2*2 = 1/2 * (a+b-10) * 2

4 = a+b-10

Add 10 to both sides.

4+10 = a+b-10+10

14 = a+b

Perimeter formula: P=a+b+c

Plug in what we know

(remember a+b=14).

P=14 + 10

P = 24

since proposition states that a number is greater than 25, if is true then the number must actually be greater than 25.

this implies that all possible options, except 24, can be accepted