The perimeter of a rectangle is 34 feet and the area measures 60 square feet.

What are the length and width of the rectangle?
(Hint: Use the equations :
perimeter = times the sum of the length and the width
area = length times width)

94

2(l+w) = 34

l+w = 17 ,#1

lw = 60 , #2

from #1, w = 17-l

in #2
l(17-l) = 60
-l^2 + 17l - 60 = 0
l^2 - 17l + 60 = 0
(l-5)(l-12) = 0

so l=5 or l=12
if l=5 then w = 12
if l=12 then w = 5

The rectangle is 5 by 12

If perimeter of garden is 2 meter mote then eight times the width of the rectangle garden. Find dimension of the garden.

To find the length and width of the rectangle, we can use the given equations for the perimeter and area.

Perimeter = 2(length + width)
Area = length * width

Given that the perimeter is 34 feet, we can set up the equation:
34 = 2(length + width)

Given that the area is 60 square feet, we can set up the equation:
60 = length * width

Now we have a system of two equations with two unknowns (length and width). We can solve this system to find the values of length and width.

We can rearrange the equation for the perimeter to get:
length + width = 34/2
length + width = 17

Next, we can use this value in the equation for the area to get:
60 = length * width

Now we have a system of equations:
length + width = 17
length * width = 60

To solve this system, we can use substitution or elimination method.

Let's use substitution method:
From the first equation, we can rearrange it to solve for length:
length = 17 - width

Now substitute this value of length into the second equation:
(17 - width) * width = 60

Simplifying this equation, we get:
17w - w^2 = 60
Rearranging the equation to get a quadratic equation, we have:
w^2 - 17w + 60 = 0

Factoring this equation, we get:
(w - 12)(w - 5) = 0

Setting each factor equal to zero, we can solve for the values of w:
w - 12 = 0 or w - 5 = 0
w = 12 or w = 5

Therefore, the possible values for the width are 12 feet and 5 feet.

If the width is 12 feet, we can substitute it back into the equation for length:
length = 17 - width
length = 17 - 12
length = 5

Therefore, if the width is 12 feet, the length is 5 feet.

If the width is 5 feet, we can substitute it back into the equation for length:
length = 17 - width
length = 17 - 5
length = 12

Therefore, if the width is 5 feet, the length is 12 feet.

So, the possible length and width of the rectangle are:
Length: 5 feet, Width: 12 feet
Length: 12 feet, Width: 5 feet