Answer :
Answer:
1. The length of the base of the rectangle is 18.9 cm.
2. The height of the rectangle is 50.4 cm.
3. The rectangle's area is 952.56 cm².
Step-by-step explanation:
Given:
The ratio of the base and height of a rectangle is 3 to 8.
And its perimeter is 138.6 cm.
Now, to write and solve an equation to find the length of the base and height.
Let the length of the base be [tex]3x.[/tex]
And let the length of the height be [tex]8x.[/tex]
Perimeter of rectangle = 138.6 cm.
Now, we put equation to get the base and height by putting formula of perimeter:
[tex]Perimeter=2\times base+2\times height[/tex]
[tex]138.6=2\times 3x+2\times 8x[/tex]
[tex]138.6=6x+16x\\\\138.6=22x[/tex]
Dividing both sides by 22 we get:
[tex]6.3=x\\\\x=6.3.[/tex]
Substituting the value of [tex]x[/tex]:
Base = [tex]3x[/tex]
= [tex]3\times 6.3=18.9\ cm.[/tex]
Height = [tex]8x[/tex]
= [tex]8\times 6.3=50.4\ cm.[/tex]
Now, to get the area of the rectangle by putting formula:
[tex]Area=base\times height\\\\Area=18.9\times 50.4\\\\Area=952.56\ cm^2.[/tex]
Therefore, 1. the length of the base of the rectangle is 18.9 cm.
2. The height of the rectangle is 50.4 cm.
3. The rectangle's area is 952.56 cm².