Math Question and Answers


Question and Answers Forum

All Questions Topic List
Geometry Questions
Previous in All Question Next in All Question
Previous in Geometry Next in Geometry
Question Number 182001 by mr W last updated on 03/Dec/22

Commented by mr W last updated on 03/Dec/22

$f i n d t h e a r e a o f t r i a n g l e .$
	Answered by som(math1967) last updated on 03/Dec/22
	$let rad of inner circle=r ∴AB=x+r BC=y+r (x+r)^2 +(y+r)^2 =(x+y)^2 x^2 +y^2 +2r^2 +2r(x+y)=x^2 +y^2 +2xy ⇒r^2 +r(x+y)=xy ar. of triangle (1/2)×(x+r)(y+r) =(1/2){xy+r(x+y)+r^2 } =(1/2)×(xy+xy)=xy=17squnit$
	$l e t r a d o f i n n e r c i r c l e = r$ $∴ A B = x + r$ $B C = y + r$ ${(x + r)}^{2} + {(y + r)}^{2} = {(x + y)}^{2}$ $x^{2} + y^{2} + 2 r^{2} + 2 r (x + y) = x^{2} + y^{2} + 2 x y$ $\Rightarrow r^{2} + r (x + y) = x y$ $a r . o f t r i a n g l e$ $\frac{1}{2} \times (x + r) (y + r)$ $= \frac{1}{2} {x y + r (x + y) + r^{2}}$ $= \frac{1}{2} \times (x y + x y) = x y = 17 s q u n i t$
	Commented by som(math1967) last updated on 03/Dec/22

	Commented by mr W last updated on 03/Dec/22

	$t h a n k s!$
	Answered by SEKRET last updated on 03/Dec/22

	$S = \frac{(r + x) (r + y)}{2} = \frac{r^{2} + r (x + y) + xy}{2} = ?$ ${(x + r)}^{2} + {(y + r)}^{2} = {(x + y)}^{2}$ $x^{2} + 2 xr + r^{2} + y^{2} + 2 yr + r^{2} = x^{2} + 2 xy + y^{2}$ $2 r (x + y) + 2 r^{2} = 2 xy$ $r^{2} + r (x + y) = xy$ $S = \frac{xy + xy}{2} = xy = 17$
	Commented by mr W last updated on 03/Dec/22

	$t h a n k s!$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum