kevinroland pisze: ↑14 kwie 2022, 09:09
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.