Answer:
The length is 48
The width is 20
Step-by-step explanation:
When 2 rectangles (figures) are similar, the ratio of corresponding sides are equal.
This rectangle is 5 by 12, so the shorter side (corresponding to 5) to the longer side (corresponding to 12) would be the same ratio, 5:12.
Let shorter side be s, and
longer side be l
It says, long side is 8 greater than twice short, we can write this as:
[tex]l=2s+8[/tex]
In similar rectangles, we have said the corresponding sides' ratio are equal, so we could write:
[tex]\frac{s}{l}=\frac{5}{12}[/tex]
Now, we replace the new found expression for "l" onto this and cross multiply and solve for s first:
[tex]\frac{s}{l}=\frac{5}{12}\\\frac{s}{2s+8}=\frac{5}{12}\\5(2s+8)=12*s\\10s+40=12s\\2s=40\\s=\frac{40}{2}\\s=20[/tex]
So the shorter side is 20. and hence the longer side would be:
l = 2s + 8
l = 2(20) + 8
l = 40 + 8
l = 48
The longer side is 48.
The length is 48
The width is 20
