Answer:
8 cm and 10 cm
Step-by-step explanation:
Hello, <em> </em>I can help you with this.
Step 1
According to the question there are two rectangles A and B,
Rectangle A is a scale drawing of Rectangle B and has 25% of its area
in other words
![Area_{A}=0.25*Area_{B} (Equation\ 1)\\](https://tex.z-dn.net/?f=Area_%7BA%7D%3D0.25%2AArea_%7BB%7D%20%28Equation%5C%201%29%5C%5C)
Step 2
Let
Rectangle A
length (1)= 4 cm
length (2)= 5 cm
![Area_{A}=4\ cm * 5\ cm\\Area_{A}=20\ cm^{2}](https://tex.z-dn.net/?f=Area_%7BA%7D%3D4%5C%20cm%20%2A%205%5C%20cm%5C%5CArea_%7BA%7D%3D20%5C%20cm%5E%7B2%7D)
put this value into equation 1
![Area_{A}=0.25*Area_{B} (Equation\ 1)\\\\20\ cm^{2} =0.25*Area_{B} \\divide\ each\ side\ by\ 0.25\\\frac{20\ cm^{2} }{0.25}=\frac{0.25}{0.25}*Area_{B}\\ Area_{B}=80\ cm^{2}](https://tex.z-dn.net/?f=Area_%7BA%7D%3D0.25%2AArea_%7BB%7D%20%28Equation%5C%201%29%5C%5C%5C%5C20%5C%20cm%5E%7B2%7D%20%3D0.25%2AArea_%7BB%7D%20%5C%5Cdivide%5C%20each%5C%20side%5C%20by%5C%200.25%5C%5C%5Cfrac%7B20%5C%20cm%5E%7B2%7D%20%7D%7B0.25%7D%3D%5Cfrac%7B0.25%7D%7B0.25%7D%2AArea_%7BB%7D%5C%5C%20%20Area_%7BB%7D%3D80%5C%20cm%5E%7B2%7D)
Now, we know the area of rectangle B, to know its length we need to formule other equation
Step 3
![Area_{B}=80\ cm^{2}\\length (1B)*length (2B)=80\ cm^{2} (equation\ 2)\\](https://tex.z-dn.net/?f=Area_%7BB%7D%3D80%5C%20cm%5E%7B2%7D%5C%5Clength%20%281B%29%2Alength%20%282B%29%3D80%5C%20cm%5E%7B2%7D%20%28equation%5C%202%29%5C%5C)
the ratio between the lengths must be constant, so the ratio of A must be equal to ratio in B, then
![\frac{length(1A)}{length(2A)}=\frac{length(1B)}{length(2B)} \\\\\\frac{4}{5}= \frac{length(1B)}{length(2B)}\\0.8=\frac{length(1B)}{length(2B)}\\length(1B)=0.8*length(2B) (Equation 3)](https://tex.z-dn.net/?f=%5Cfrac%7Blength%281A%29%7D%7Blength%282A%29%7D%3D%5Cfrac%7Blength%281B%29%7D%7Blength%282B%29%7D%20%20%5C%5C%5C%5C%5C%5Cfrac%7B4%7D%7B5%7D%3D%20%5Cfrac%7Blength%281B%29%7D%7Blength%282B%29%7D%5C%5C0.8%3D%5Cfrac%7Blength%281B%29%7D%7Blength%282B%29%7D%5C%5Clength%281B%29%3D0.8%2Alength%282B%29%20%28Equation%203%29)
Step three
using Eq 1 and Eq 2 find the lengths
put the value of length(1B) into equation (2)
![length (1B)*length (2B)=80\ cm^{2} (equation\ 2)\\\(0.8*length(2B)) (*length (2B)=80\ cm^{2} \\\\0.8*(length (2B))^{2} =80\ cm^{2}\\(length (2B))^{2} =\frac{80\ cm^{2}}{0.8} \\(length (2B))^{2}=100\\\sqrt{(length (2B))^{2}}=\sqrt{100\ cm^{2}} \\ length (2B)=10\ cm](https://tex.z-dn.net/?f=length%20%281B%29%2Alength%20%282B%29%3D80%5C%20cm%5E%7B2%7D%20%28equation%5C%202%29%5C%5C%5C%280.8%2Alength%282B%29%29%20%28%2Alength%20%282B%29%3D80%5C%20cm%5E%7B2%7D%20%5C%5C%5C%5C0.8%2A%28length%20%282B%29%29%5E%7B2%7D%20%3D80%5C%20cm%5E%7B2%7D%5C%5C%28length%20%282B%29%29%5E%7B2%7D%20%3D%5Cfrac%7B80%5C%20cm%5E%7B2%7D%7D%7B0.8%7D%20%5C%5C%28length%20%282B%29%29%5E%7B2%7D%3D100%5C%5C%5Csqrt%7B%28length%20%282B%29%29%5E%7B2%7D%7D%3D%5Csqrt%7B100%5C%20cm%5E%7B2%7D%7D%20%5C%5C%20length%20%282B%29%3D10%5C%20cm)
Now, put the value of length(2B) into equation 3 to know length (1B)
![length(1B)=0.8*length(2B)\\length(1B)=0.8*10\ cm\\length(1B)=8 cm](https://tex.z-dn.net/?f=length%281B%29%3D0.8%2Alength%282B%29%5C%5Clength%281B%29%3D0.8%2A10%5C%20cm%5C%5Clength%281B%29%3D8%20cm)
I really hope this helps you, have a great day.