jest prostokąt

[kevinroland]

Dany jest prostokąt o bokach długości 2 cm i 7 cm. Oblicz pole prostokąta podobnego do niego, wiedząc że jego
obwód jest równy 24 cm.

Proszę... o pomoc.

[eresh]

Dany jest prostokąt o bokach długości 2 cm i 7 cm. Oblicz pole prostokąta podobnego do niego, wiedząc że jego
obwód jest równy 24 cm.

Proszę... o pomoc.

\(\frac{24}{2\cdot 2+2\cdot 7}=k\\
\frac{4}{3}=k\)

\(\frac{P}{2\cdot 7}=k^2\\
P=\frac{16}{9}\cdot 14\\
P=\frac{224}{9}\)

[ann77]

Dany jest prostokąt o bokach długości 2 cm i 7 cm. Oblicz pole prostokąta podobnego do niego, wiedząc że jego
obwód jest równy 24 cm.

Proszę... o pomoc.

We can begin by using the fact that similar figures have proportional side lengths. Let the length of one side of the new rectangle be x cm. Since the new rectangle is similar to the original rectangle, we can write:

\({x\over2} = {x + 7\over7}\)

We can solve for x by cross-multiplying:

\(7x = 2(x + 7)\\

7x = 2x + 14\\

5x = 14\\

x = 2.8\)

So, the length of the longer side of the new rectangle is \(2.8 + 7 = 9.8\) cm. The area of the new rectangle is:

\((2.8 \text{ cm}) x (9.8 \text{ cm}) = 27.44 \text{ cm}^2\)

Therefore, the area of the new rectangle is \(27.44\) square centimeters.

[Jerry]

... we can write:
\({x\over2} = {x + 7\over7}\)

Why, it is inconsistent with the content of the task! It would be correct:
\(\begin{cases}{x\over2} = {y\over7}\\2x+2y=24\end{cases}\So {x\over2} = {12-x\over7}\)

I greet You

[Aarshi]

We can begin by using the fact that similar figures have proportional side lengths. Let the length of one side of the new rectangle be x cm. Since the new rectangle is similar to the original rectangle, we can write:

\({x\over2} = {x + 7\over7}\)

We can solve for x by cross-multiplying:

\(7x = 2(x + 7)\\

7x = 2x + 14\\

5x = 14\\

x = 2.8\)

So, the length of the longer side of the new rectangle is \(2.8 + 7 = 9.8\) cm. The area of the new rectangle is:

\((2.8 \text{ cm}) x (9.8 \text{ cm}) = 27.44 \text{ cm}^2\)

Therefore, the area of the new rectangle is \(27.44\) square centimeters.

Excellent explanation! Clear, concise, and accurate. Well done in solving for x and determining the area of the new rectangle. Impressive work!

[Jerry]

Therefore, the area of the new rectangle is \(27.44\) square centimeters.

Excellent explanation! Clear, concise, and accurate. Well done in solving for x and determining the area of the new rectangle. Impressive work!

Really?

I gret You