the area of a certain rectangle is 288 yd squared. the perimeter is 68 yards. double the length and width what will be the area and perimeter of the new rectangle
Area (A) = Lw = 288
Perimeter (P) = 2L + 2w = 68
L = length, w = width
Solve 2L + 2w = 68 for either L or w
I'll choose L
2L + 2w = 68
2L = 68 - 2w
2L = 2(34 - w)
L = 34 - w
Substitute L = 34 - w, for L in
A = Lw = 288
(34 - w)(w) = 288
34w - w^2 = 288
w^2 - 34w + 288 = 0
w = 18, 16
So, this certain rectangle has dimensions of 18 by 16.
you should be able to calculate the area and perimeter of the new rectangle now. (double the length and width and solve the equations)
r = 2/3t + v, for t
A=1120yd squared P= 134yd squared
To find the area and perimeter of the new rectangle after doubling the length and width, we can start by solving the given information.
Let's assume the length of the original rectangle is 'L' yards and the width is 'W' yards.
We know that the area of a rectangle is given by the formula:
Area = Length × Width
According to the given information, the area of the rectangle is 288 yd², so we have:
288 = L × W ---(equation 1)
We also know that the perimeter of a rectangle is given by the formula:
Perimeter = 2 × (Length + Width)
According to the given information, the perimeter of the rectangle is 68 yards, so we have:
68 = 2 × (L + W) ---(equation 2)
Now, let's solve equations 1 and 2 simultaneously to find the values of L and W.
From equation 2, we can rewrite it as: L + W = 34 ---(equation 3)
Now we have two equations: equation 1 (288 = L × W) and equation 3 (L + W = 34).
To find the values of L and W, we can use different methods such as substitution or elimination. In this case, let's use substitution.
From equation 3, we can rewrite it as: W = 34 - L
Now substitute this value of W in equation 1:
288 = L × (34 - L)
Simplifying further:
288 = 34L - L²
Rearranging the equation:
L² - 34L + 288 = 0
Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula to find the values of L. For simplicity, let's use factoring to find the roots.
Factoring the equation above, we get:
(L - 18)(L - 16) = 0
Setting each factor to zero, we find:
L - 18 = 0 or L - 16 = 0
Solving these two equations, we find the values of L as:
L = 18 or L = 16
Now, substitute these values back into equation 3 or equation 2 to find the corresponding values of W.
For L = 18, W = 34 - 18 = 16
For L = 16, W = 34 - 16 = 18
So, we have two possibilities for our original rectangle:
Option 1: Length = 18 yards, Width = 16 yards
Option 2: Length = 16 yards, Width = 18 yards
Now, to find the new rectangle after doubling the length and width, we multiply each dimension by 2.
For Option 1:
New Length = 2 × 18 = 36 yards
New Width = 2 × 16 = 32 yards
For Option 2:
New Length = 2 × 16 = 32 yards
New Width = 2 × 18 = 36 yards
Now, we can calculate the area and perimeter of both new rectangles.
For Option 1:
New Area = New Length × New Width = 36 × 32 = 1152 yd²
New Perimeter = 2 × (New Length + New Width) = 2 × (36 + 32) = 2 × 68 = 136 yards
For Option 2:
New Area = New Length × New Width = 32 × 36 = 1152 yd² (same as Option 1)
New Perimeter = 2 × (New Length + New Width) = 2 × (32 + 36) = 2 × 68 = 136 yards (same as Option 1)
Therefore, regardless of which option, the area of the new rectangle is 1152 yd², and the perimeter is 136 yards.