Respuesta :
Answer:
Length = 5 yards and Width = 2 yards.
Step-by-step explanation:
Given:
The area of a playground is 20 yd.²
The length of the playground at five times longer than it's width.
Question asked:
Find the length and the width of the playground.
Solution:
Let width of the playground = [tex]x[/tex]
Then, length of the playground = [tex]5x[/tex]
As we know:
[tex]Area \ of\ rectangle=length\times width[/tex]
[tex]20=5x\times x\\20=5x^{2} \\Dividing\ both \ sides\ by\ 5\\\\ x^{2} =4\\Taking\ root\ both\ sides\\ \\ \sqrt[2]{x^{2} } =\sqrt[2]{4} \\ \\ x=\sqrt[2]{2\times2} \\ \\ x=2[/tex]
By substituting the value:-
width of the playground = [tex]x[/tex] = 2 yards
length of the playground = [tex]5x[/tex] = [tex]5\times2=10\ yards[/tex]
Therefore, the length and the width of the playground is 5 yards and 2 yards.
