Three congruent rectangles are placed to form a larger rectangle as shown with an area of 1350cm^2 Find the area of a square that has the same perimeter as the larger rectangle?
let's say the larger sides of the small rectangles are the bases of the small rectangles, we'll call the bases
let's say the larger sides of the large rectangle are the bases of the large rectangle, we'll call those bases
Same thing for height.
Now you know that the area of any rectangle is base times height, so since the three rectangles are congruent, you know that: (make sure to check my arithmetic)
Look at the picture, you also know that:
Also:
Substitute:
Multiply both sides by to get:
Substitute:
Divide:
Find the square root of both sides:
Now you know that:
So:
Alright, you also know that:
Substitute:
Divide:
So the perimeter of the Larger rectangle is:
So let's call the sides of the square
Therefore:
So the area of the square is:
But MAKE SURE TO CHECK MY ARITHMETIC!!!!!!!!!!!
Hello, Dragon!
My solution is the same as Quick's . . . without the subscripts.
Three congruent rectangles are placed to form a larger rectangle
. . as shown with an area of 1350 cm^2
Find the area of a square that has the same perimeter as the larger rectangle.
Let = length of the small rectangles
and = width of the small rectangles.Code:y x * - - - - + - - - - - - - * | | | | | | y | | | x | + - - - - - - - + | | | | | | y | | | * - - - - + - - - - - - - * y x
Since the left and right sides are equal:
. . and the rectangle looks like this:Code:3y * - - - - - - - - - - - - * | | | | | | 2y | | 2y | | | | | | * - - - - - - - - - - - - * 3y
Its area is: .
Its perimeter is: .
Since the area is 1350 cm², we have: .
And its perimeter is: . cm.
The square with the same perimeter has a side of: cm.
The area of this square is: .