Answer:
5m by 12m
Step-by-step explanation:
Let A represent the area, L, the Length and W, the width of the garden with dimension 3m by 10m
Area of a rectangle, A = LW
Area of the garden with the old dimension = 3(10) = 30 sq meters
Let A1 represent the area, L1 represent the length and W1, the width of the new dimension of the garden
Since the dimensions were increased by equal amounts, lets call this amount x, the area of the garden doubled
This means,
A1 = 2A
Put in the value of A
A1= 2 (30)
A1 = 60 sq units
and
L1 = L + x
W1 =W + x
Therefore, to find the new area, we have;
A1 = ( L + x ) ( W+x )
60 = ( 3 + x ) ( 10 + x )
expand the bracket
60 = 30 + 3x + 10x + x^2
60 = 30 + 13x + x^2
Subtract 30 from both sides
60 - 30 = 30 -30 + 13x + x^2
30 = 13x +x^2
Equate to zero to form a quadratic equation
x^2 + 13x - 30 = 0
Now, lets think of two numbers that when multiplied they give -30 and when summed give +13
Yes! it's +15 and -2
Noe lets solve the equation
x^2 + 15x - 2x - 30 = 0
x( x + 15 ) -2 ( x + 15 ) = 0
( x - 2 ) ( x + 15) = 0
x - 2= 0
x = 2
x + 15 = 0
x = -15
Since we can only use the positive value of x, therefore x = 2m
To get the new dimension
Remember that;
L1 = L + x
slot in the value of L
L1 = 3 + 2
L1 = 5m
slot in the value of W
W1 = W + x
W1 = 10 + 2
W1 = 12m
Hence, the new dimension is 5m by 12m
