Respuesta :
Answer:
[tex]\text{Smaller square's 15 inches, Bigger square's 18 inches}[/tex]
Step-by-step explanation:
GIVEN: The length of each side of a square is [tex]3[/tex] inches more than the length of each side of a small square. The sum of the areas of the square is [tex]549[/tex] inches.
TO FIND: the lengths of the sides of the two squares.
SOLUTION:
let the length of side of small square be [tex]\text{x}[/tex]
Area of small square [tex]=(\text{side})^2=\text{x}^2[/tex]
As length of each side of bigger square is [tex]3\text{ inches}[/tex] more than the smaller square
length of side of bigger square [tex]=\text{x}+3\text{ inches}[/tex]
Area of bigger square [tex]=(\text{x+3})^2[/tex]
Also
Sum of areas of both square [tex]=549\text{ inch}^2[/tex]
[tex](\text{x})^2+(\text{x+3})^2=549[/tex]
[tex]2\text{x}^2+6\text{x}+9=549[/tex]
[tex]\text{x}^2+3\text{x}-270=0[/tex]
[tex]\text{x}=15,-18[/tex]
as the length of side can never be negative
[tex]\text{x}=15[/tex]
length of side of smaller square [tex]=15\text{ inches}[/tex]
length of side of bigger square [tex]=\text{x}+3\text{ inches}[/tex][tex]=18\text{ inches}[/tex]
Hence the length of smaller and bigger square are [tex]15\text{ inches}[/tex] and [tex]18\text{ inches}[/tex] respectively.
