Introduction to Rectangle:
A Rectangleis any quadrilateral with four right angles. The term "oblong" is occasionally used to refer to a non-square rectangle. A rectangle with vertexes ABCD would be denoted as ABCD.
We shall work out some problems on rectangles
Rectangle word problem 1:
A rectangle has a perimeter of 120 meters and its length L is 2 times its width W. Calculate the dimensions W and L, and the area of the rectangle.
Solution to rectangle word problem 1:
The formula to find the perimeter of rectangle is
2 L + 2 W = 120
Now, we rewrite the statement, length L is 2 times its width “w” into a mathematical equation as follows,
L = 2 W
We substitute L in the equation 2 L + 2 W = 120 by 2 W.
2(2 W) + 2 W = 120
Expand and group like terms.
6 W = 120
Solve for W.
W = 20 meters
Use the equation L = 2 W to find L.
L = 2 W = 40 meters
Use the formula of the area.
Area = L W = 40 * 20 = 800 meters 2
Rectangle word problem 2:
The perimeter of a rectangle is 70 feet and its area is 304 feet 2. Find the length L and the width W of the rectangle, such that L > W.
Solution for rectangle word problem 2:
The formula for perimeter of a rectangle is given by
2 L + 2 W = 70
and the formula area of a rectangle is given by
L W = 304
Divide all terms in the equation 2 L + 2 W = 35 by 2 to obtain
L + W = 35
Solve the above for W
W = 35 - L
Substitute W by 35 - L in the equation L W = 304
L(35 - L) = 304
Expand the above equation and rewrite with right term equal to zero.
-L 2 + 35 L - 304 = 0
The above is a quadratic equation with two solutions.
L = 16 and L = 19
Use W = 35 - L to find the corresponding values of W.
W = 19 and W = 16
Since L > W, the rectangle has the dimensions
L = 19 feet and W = 16 feet.
Practice rectangle word problem 1:
The perimeter of a rectangle is 90 feet and its area is 504 feet 2. Find the length L and the width W of the rectangle, such that L > W.
Practice rectangle word problem 2:
A rectangle has a perimeter of 240 meters and its length L is 5 times its width W. Calculate the dimensions W and L, and the area of the rectangle
A Rectangleis any quadrilateral with four right angles. The term "oblong" is occasionally used to refer to a non-square rectangle. A rectangle with vertexes ABCD would be denoted as ABCD.
We shall work out some problems on rectangles
Rectangle word problem 1:
A rectangle has a perimeter of 120 meters and its length L is 2 times its width W. Calculate the dimensions W and L, and the area of the rectangle.
Solution to rectangle word problem 1:
The formula to find the perimeter of rectangle is
2 L + 2 W = 120
Now, we rewrite the statement, length L is 2 times its width “w” into a mathematical equation as follows,
L = 2 W
We substitute L in the equation 2 L + 2 W = 120 by 2 W.
2(2 W) + 2 W = 120
Expand and group like terms.
6 W = 120
Solve for W.
W = 20 meters
Use the equation L = 2 W to find L.
L = 2 W = 40 meters
Use the formula of the area.
Area = L W = 40 * 20 = 800 meters 2
Rectangle word problem 2:
The perimeter of a rectangle is 70 feet and its area is 304 feet 2. Find the length L and the width W of the rectangle, such that L > W.
Solution for rectangle word problem 2:
The formula for perimeter of a rectangle is given by
2 L + 2 W = 70
and the formula area of a rectangle is given by
L W = 304
Divide all terms in the equation 2 L + 2 W = 35 by 2 to obtain
L + W = 35
Solve the above for W
W = 35 - L
Substitute W by 35 - L in the equation L W = 304
L(35 - L) = 304
Expand the above equation and rewrite with right term equal to zero.
-L 2 + 35 L - 304 = 0
The above is a quadratic equation with two solutions.
L = 16 and L = 19
Use W = 35 - L to find the corresponding values of W.
W = 19 and W = 16
Since L > W, the rectangle has the dimensions
L = 19 feet and W = 16 feet.
Practice rectangle word problem 1:
The perimeter of a rectangle is 90 feet and its area is 504 feet 2. Find the length L and the width W of the rectangle, such that L > W.
Practice rectangle word problem 2:
A rectangle has a perimeter of 240 meters and its length L is 5 times its width W. Calculate the dimensions W and L, and the area of the rectangle
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