The perimeter of a polygon is the sum of the measures of its sides.
A rectangle is a quadrilateral such that all angles measure 90°. Also, a rectangle has congruent opposite sides, called length and width. Therefore, in a rectangle, 2 sides are called length, and the other 2 sides are called width.
Since the perimeter is the sum of all the measure of its sides, we can add the lengths and widths of the rectangle. Let l be the length and w be the width of the rectangle; its perimeter is expressed by
perimeter : l +l +w+w
perimeter: 2l + 2w
The perimeter of the rectangle is 56. We also know that one side is 5cm less than twice the other. Let's say the length is that one side.
l=2w- 5
"5 less than" means decreasing something by 5
"twice" means multiplying by 2.
We can now substitute these values to the perimeter expression from earlier.
perimeter: 2l+2w
perimeter: 56
l=2w-5
56=2(2w-5)+2w
56=4w-10+2w
56=6w-10
56+10=6w
66w=6w
w=11
We now know that w = 11. Substituting it back to the expression gives us l.
l=2w-5
l=2(11)-5
l=22-5
l=17
We now also know that l = 17.
The dimensions of the rectangle are 17cm and 11cm.
The area of a rectangle is given by the formula:
l*w
Since we know the length and width of the rectangle, we can multiply them.
Answers & Comments
Answer:
dimensions = 17 cm and 11 cm
area = 187 cm^2
Step-by-step explanation:
The perimeter of a polygon is the sum of the measures of its sides.
A rectangle is a quadrilateral such that all angles measure 90°. Also, a rectangle has congruent opposite sides, called length and width. Therefore, in a rectangle, 2 sides are called length, and the other 2 sides are called width.
Since the perimeter is the sum of all the measure of its sides, we can add the lengths and widths of the rectangle. Let l be the length and w be the width of the rectangle; its perimeter is expressed by
perimeter : l +l +w+w
perimeter: 2l + 2w
The perimeter of the rectangle is 56. We also know that one side is 5cm less than twice the other. Let's say the length is that one side.
l=2w- 5
"5 less than" means decreasing something by 5
"twice" means multiplying by 2.
We can now substitute these values to the perimeter expression from earlier.
perimeter: 2l+2w
perimeter: 56
l=2w-5
56=2(2w-5)+2w
56=4w-10+2w
56=6w-10
56+10=6w
66w=6w
w=11
We now know that w = 11. Substituting it back to the expression gives us l.
l=2w-5
l=2(11)-5
l=22-5
l=17
We now also know that l = 17.
The dimensions of the rectangle are 17cm and 11cm.
The area of a rectangle is given by the formula:
l*w
Since we know the length and width of the rectangle, we can multiply them.
area= l*w
area=17*11
area= 187
the rectangle of rose is 187cm^2