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A triangle ABC, right angled at B, is inscribed with a circle having 4cm diameter. The side BC is 5cm. What is the perimeter of the triangle?

Answer 1

Julia Adams

Perimeter of the triangle is #30# cm.

In right angle #Delta ABC , AB, BC,AC# are perpendicular (p),

base (b) and hypotenuse (h), correspondingly. The incircle's radius

is #r=4/2=2# cm , #BC=b=5# cm. In-radius of R.A.T is

# r=(p+b-h)/2 :. (p+5-h)/2=2 or p+5-h=4 #

#h= p+1 ; h^2= p^2+b^2 or h^2= p^2+25#(Pythagoras formula).

or # (p+1)^2 =p^2 +25 or cancel(p^2)+2 p+1= cancel(p^2)+25#

#:.2 p= 24 or p = 12 :. h= sqrt( 12^2+5^2)=13 #

#p=12,b=5,h=13 #. Perimeter of the triangle is

#T_p= (p+b+h)= 12+5+13=30# cm. [Ans]

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Answer 2

Jameson Allen

The perimeter of the triangle is 20 cm.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.