Answer: 160ft.
Explanation:
First find the area of the 48ft x 100ft rectangular back yard.
Area of a rectangular = L x B
= 48 x 100
= 4800ft²
Now, find 1/4 of the rectangular backyard meant for garden
= 1/4 of 4800
= 1200ft²
Step 2:
To find the perimeter of the garden,first find the length and breath of the garden. From the dimension of the garden, the length is 40ft > width. In interpreting this,
We make the width of the garden to be. B = xft,
Therefore. L = (x + 40)ft
Now equate the product of this to 1200ft
x(x + 40) = 1200
Open the bracket
x² + 40x = 1200
x² + 40x - 1200 = 0
This is now a quadratic expression. Solving for x using any methods
x² + 60x - 20x - 1200 = 0
Solving by grouping
x(x + 60) - 20(x + 60) = 0
Collect common factors here
(x + 60)(x - 20) = 0
Therefore, x = -60 or 20
Remember, x cannot be negative, so x = 20ft. The width = 20ft, and the length = 60ft.
With this, we can determine the perimeter.
Formula for perimeter of a rectangular block
= 2( L + B )
= 2( 60 + 20 )
= 2(80)
= 2 x 80
= 160ft.