Задание 194

Question

Площадь прямоугольника равна 360 м$^2$ , а его периметр равен 76 м. Найдите стороны прямоугольника.

Gimli · Accepted Answer

\begin{align*}
\left\{\begin{array}{rc1}{ab = 360}\{2a + 2b = 76}\end{array}ight.
&\iff  \left\{\begin{array}{rc1}{ab = 360}\{a + b = 38}\end{array}ight.\
&\iff  \left\{\begin{array}{rc1}{ab = 360}\{a = 38 - b}\end{array}ight.\ &\iff  \left\{\begin{array}{rc1}{(38 - b)b = 360}\{a = 38 - b}\end{array}ight.\
&\iff  \left\{\begin{array}{rc1}{38b - b^2 = 360}\{a = 38 - b}\end{array}ight.\
&\iff  \left\{\begin{array}{rc1}{-b^2 + 38b - 360 = 0*}\{a = 38 - b}\end{array}ight.\
&\iff  \left\{\begin{array}{rc1}{b_1 = 18}\{a = 38 - 18 = 20}\end{array}ight.
\end{align*}
$$	ext{или} \left\{\begin{array}{rc1}{b_2  = 20}\{a = 38 - 20 = 18}\end{array}ight.$$
	extbf{______________________________}
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	*РЕШЕНИЕ УРАВНЕНИЯ $-b^2 + 38b - 360 = 0$:
$$D = 38^2 - 360\cdot 4 = 1444 - 1440 = 2^2$$
$$b_1 = \frac{-38 + 2}{-2} = \frac{-36}{-2} = 18$$
$$b_2 = \frac{-38 - 2}{-2} = \frac{-40}{-2} = 20$$

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	extbf{Ответ: стороны прямоугольника равны 18 и 20 м.}

Задание 194

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Задание 194

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