15 uždavinys
Sprendimas.
Stataus trikampio ploto formulė pagal įbrėžto apskritimo spindulį $$S = r\cdot p$$
Į statųjį trikampį įbrėžto apskritimo spindulio formulė
$$r = \frac{a+b-c}{2}$$
r =
| (a+b-c) |
| / 2 |
|
r =
$$r$$ = $$\frac{a+b-c}{2}$$
| (a+b-c) |
| / 2 |
Paaiškinimas: Keitimas $${\normalsize c}$$ = $${\normalsize (2\cdot c-c)}$$.
r =
$$r$$ = $$\frac{a+b-(2\cdot c-c)}{2}$$
| (a+b-( 2* c-c)) |
| / 2 |
$${\normalsize -(2\cdot c-c)}$$ = $${\normalsize 2\cdot c+c}$$
r =
$$r$$ = $$\frac{a+b-2\cdot c+c}{2}$$
| (a+b- 2* c+c) |
| / 2 |
r =
$$r$$ = $$\frac{a+b+c-2\cdot c}{2}$$
| (a+b+c- 2* c) |
| / 2 |
2* r = a+b+c- 2* c$$2\cdot r$$ = $$a+b+c-2\cdot c$$
2* r+ 2* c = a+b+c$$2\cdot r+2\cdot c$$ = $$a+b+c$$
$${\normalsize 2\cdot r+2\cdot c}$$ = $${\normalsize 2\cdot (r+c)}$$ Paaiškinimas:
Paaiškinimas: 2 iškeltas prieš skliaustus, skliaustuose liko $${\normalsize r+c}$$.
2* (r+c) = (a+b+c)$$2\cdot (r+c)$$ = $$(a+b+c)$$
(r+c) =
$$(r+c)$$ = $$\frac{a+b+c}{2}$$
| (a+b+c) |
| / 2 |
$$r$$ = $$\frac{a+b-c}{2}$$
$$r$$ = $$\frac{a+b-(2\cdot c-c)}{2}$$
$$r$$ = $$\frac{a+b-2\cdot c+c}{2}$$
$$2\cdot r$$ = $$a+b+c-2\cdot c$$
$$2\cdot r+2\cdot c$$ = $$a+b+c$$
$$2\cdot (r+c)$$ = $$(a+b+c)$$
$$(r+c)$$ = $$\frac{a+b+c}{2}$$
Trikampio pusperimetris p = r+c.
Trikampio plotas yra
S =
r* p
r* p
|
|
S = r* p$$S$$ = $$r\cdot p$$
Paaiškinimas: Keitimas $${\normalsize p}$$ = $${\normalsize r+c}$$.
S = r* (r+c)$$S$$ = $$r\cdot (r+c)$$
Paaiškinimas: Keitimas $${\normalsize r}$$ = $${\normalsize 2}$$.
S = 2* (2+c)$$S$$ = $$2\cdot (2+c)$$
Paaiškinimas: Keitimas $${\normalsize c}$$ = $${\normalsize 10}$$.
S = 2* (2+10)$$S$$ = $$2\cdot (2+10)$$
$${\normalsize 2+10}$$ = $${\normalsize 12}$$
S = 2* (12)$$S$$ = $$2\cdot (12)$$
$${\normalsize 2\cdot (12)}$$ = $${\normalsize 24}$$
S = 24$$S$$ = $$24$$
$$S$$ = $$r\cdot p$$
$$S$$ = $$r\cdot (r+c)$$
$$S$$ = $$2\cdot (2+c)$$
$$S$$ = $$2\cdot (2+10)$$
$$S$$ = $$2\cdot (12)$$
$$S$$ = $$24$$
Atsakymas: 24