The length of a rectangle is 8 cm longer than its width , if the perimeter is 84 cm , what is its area
84= 2L+2W=2L+2(L-8)=4L-16
L=(84+16)/4=25 check that
area then = L*W
To find the area of a rectangle, we need to know the length and width of the rectangle. In this case, we know that the length of the rectangle is 8 cm longer than its width. Let's use "w" to represent the width of the rectangle.
Let's start by finding the value of the width. We can set up an equation using the information given. The perimeter of a rectangle is equal to twice the sum of its length and width. In this case, the perimeter is given as 84 cm.
Perimeter = 2 x (Length + Width)
84 = 2 x (w + (w + 8))
Now let's solve this equation to find the value of "w" which represents the width.
84 = 2(2w + 8)
42 = 2w + 8
34 = 2w
w = 17
Therefore, the width of the rectangle is 17 cm.
Now, since the length is given as 8 cm longer than the width, we can find the length.
Length = Width + 8 = 17 + 8 = 25
The length of the rectangle is 25 cm.
Now that we have both the length and width, we can calculate the area of the rectangle.
Area = Length x Width
Area = 25 cm x 17 cm
Area = 425 cm^2
So, the area of the rectangle is 425 square cm.