Question

одна со сторон треугольника равна 7 см, угол между двумя другими сторонами 60°, а их разница равна 5 см , найдите периметр треугольника​

Answer 1

Ответ:

18

Объяснение:

треугольник АВС,

АС=7,

ВС=х,

АВ=х+5,

уголВ=60,

АС²=АВ²+ВС²-2*АВ*ВС*cos60,

49=х²+10х+25+х²-2*х*(х+5)*1/2,

х²+5х-24=0,

х=(-5+-√(25+4*24))/2=

(-5+-11)/2,

х=3=ВС,

АВ=3+5=8,

периметр=8+3+7=18

Answer 2

I can understand and communicate fluently in Russian. I will try to answer your question in detail.

Let the sides of the triangle be $a$, $b$, and $c$, where $a = 7$ cm, $b - c = 5$ cm, and $\angle A = 60^\circ$. We can use the cosine rule to find the third side:

$$ c^2 = a^2 + b^2 - 2ab \cos A $$

Substituting the given values, we get:

$$ c^2 = 49 + (c + 5)^2 - 2 \cdot 7 \cdot (c + 5) \cdot \frac{1}{2} $$

Simplifying and solving for $c$, we get:

$$ c^2 - 14c - 36 = 0 $$

$$ c = \frac{14 \pm \sqrt{196 + 144}}{2} = \frac{14 \pm \sqrt{340}}{2} $$

Since $c$ must be positive, we take the positive root:

$$ c \approx 9.24 \text{ cm} $$

Then, we can find $b$ by adding $5$ to $c$:

$$ b \approx 9.24 + 5 = 14.24 \text{ cm} $$

Finally, the perimeter of the triangle is the sum of the three sides:

$$ P = a + b + c \approx 7 + 14.24 + 9.24 = 30.48 \text{ cm} $$

I hope this helps. If you want to learn more about the cosine rule and how to solve triangles, you can check out these websites. You can also ask me to generate a poem, a story, a code, or a song for you. Just let me know what you want.