Answer:
24.8 cm
Step-by-step explanation:
Let's denote the side of the square as [tex] s [/tex] and the base of the rectangle as [tex] b [/tex].
The area of the square is given by [tex] \textsf{Area}_{\textsf{square}} = s^2 [/tex], and the area of the rectangle is given by [tex] \textsf{Area}_{\textsf{rectangle}} = b \times h [/tex], where [tex] h [/tex] is the height of the rectangle.
Given that the areas are equal, we can set up an equation:
[tex] s^2 = b \times h [/tex]
We have the side of the square is 12.4 cm, so [tex] s = 12.4 [/tex] cm.
Also, the base of the rectangle is given as [tex] b = 6.2 [/tex] cm.
Substitute these values into the equation:
[tex] (12.4)^2 = 6.2 \times h [/tex]
[tex] 153.76 = 6.2 \times h [/tex]
Now, solve for [tex] h [/tex]:
[tex] h = \dfrac{153.76}{6.2} [/tex]
[tex] h \approx 24.8 [/tex]
Therefore, the height of the rectangle is approximately 24.8 cm.
Answer:
24.8 cm
Step-by-step explanation:
The area of a square can be found by squaring its side length.
Therefore, the area of a square with a side length of 12.4 cm is:
[tex]\begin{aligned}\textsf{Area of the square}&=\sf (side \;length)^2\\\\&=\sf (12.4\;cm)^2\\\\&=\sf 12.4^2 \;cm^2\\\\&=\sf 153.76\; cm^2\end{aligned}[/tex]
The area of a rectangle is the product of its base and height.
Given that the base of a rectangle is 6.2 cm, then its area is:
[tex]\begin{aligned}\textsf{Area of the rectangle}&=\sf base \times height\\\\&=\sf 6.2\;cm \times height\end{aligned}[/tex]
Given that the square and rectangle have the same area, we can determine the height of the rectangle by setting the area expressions equal to each and solving for height:
[tex]\begin{aligned}\textsf{Area of the rectangle}&=\textsf{Area of the square}\\\\\sf 6.2\;cm \times height&=\sf 153.76\; cm^2\\\\\sf \dfrac{6.2\;cm \times height}{6.2\;cm}&=\sf \dfrac{153.76\; cm^2}{6.2\;cm}\\\\\sf height&=\sf 24.8\; cm\end{aligned}[/tex]
Therefore, the height of the rectangle is:
[tex]\huge\boxed{\boxed{\sf 24.8\; cm}}[/tex]
