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A rectangle has length triple the side of this square and width two units less than the side of this square if the two areas are equal what are the squares dimensions?
S = side of the square
S2 = area of the square
3S = length of the rectangle
S-2 = width of the rectangle
3S (S-2) = area of the rectangle
Since the areas are equal . . .
3S (S-2) = S2
Eliminate parentheses on the right side:
3S2 - 6S = S2
Subtract S2 from each side:
2S2 - 6S = 0
Factor the left side:
S (2S - 6) = 0
S = 0 is the trivial solution. The other, useful solution is
2S - 6 = 0
S - 3 = 0
S = 3
Check:
Square: Area = S2 = 9
Rectangle: Area = 3S (S-2) = 9 (1) = 9
The areas are equal. yay!
What else can I help you with?
Is a rectangle always a square why?
No. The square is a special case of rectangle where all the sides are of equal length. So some rectangles are squares, and all squares are rectangles.
Why are all squares rectangles but not all rectangles squares?
Look at the definition of a square and a rectangle, and it should become quite clear. Briefly, a rectangle may, or may not, have sides of different length. If it does have sides of different length, then it is not a square.
Area to get the surface area of a rectangle?
Multiply the length by the width. If the rectangle is a square the two dimensions will be the same
What are the dimensions of a rectangle with a perimeter of 36 and a area of 81?
Length = 9 Width = 9 Your rectangle is a square.
How do you count the number of squares crossed by the diagonal in a rectangle?
To find the length of a diagonal in a rectangle, use the Pythagorean method. Diagonal length = square root(length squared + height squared).
What is the area of a rectangle with a length of 35m and a width of 35m?
Area = 35*35 = 1225 square m With the dimensions given it is not a rectangle but it is a square <><><><> Above is correct- but squares are also rectangles.
What are the dimensions of the rectangle with this perimeter and an area of 8000 squares meters?
what are the dimensions of the rectangle with this perimeter and an area of 8000 square meters
Is a rectangle always a square why?
No. The square is a special case of rectangle where all the sides are of equal length. So some rectangles are squares, and all squares are rectangles.
What makes square and rectangle the same?
They are not technically the same. A square is a rectangle but a rectangle is not a square. A rectangle requires opposite sides to be the same length. A square's opposite sides are the same length so it is a rectangle. A square requires all sides to be the same length, not just opposite sides. So most rectangles are not squares.
Why are all squares rectangles but not all rectangles squares?
Look at the definition of a square and a rectangle, and it should become quite clear. Briefly, a rectangle may, or may not, have sides of different length. If it does have sides of different length, then it is not a square.
How is a square a rectangle?
A square is a rectangle because the definition of a rectangle is that it has four straight sides and the opposite sides are equal in length. Squares have four straight sides, and their opposite sides match up in length. Therefore, a square is also a rectangle.
Area to get the surface area of a rectangle?
Multiply the length by the width. If the rectangle is a square the two dimensions will be the same
What are the dimensions of a rectangle with a perimeter of 36 and a area of 81?
Length = 9 Width = 9 Your rectangle is a square.
How much square ins is a rectangle?
Without the dimensions, we won't be able to tell. The area of a rectangle is the length times the width. If those dimensions are in inches, the area will be in square inches.
Is a retangle a square or is a square a rectangle?
A square is a rectangle, rectangles don't have to be squares but squares have to be rectangles.
Why a square can be rectangle and rectangle can not be square?
The above statement is not true since some rectangles ARE squares. Squares are a special type of a rectangle - one in which all sides are of equal length. In other words, the set of all squares is a subset of the set of all rectangles.
The length of a rectangle is 5 feet longer than its width The area of the rectangle is 374 square feet What are the dimensions of the rectangle?
17 and 22
