Question

city purchases a square plot of land with an area of (x2+ 24x + 144) square yards for a park. The dimensions of the plot are of the form ax + b, where a and b are whole numbers. Find an expression in terms of x for the perimeter of the park. An expression in terms of x for the perimeter of the park is Select... select 8) The perimeter of the park when x = 10 yards

Answer 1

Area has been given as (x² + 24x + 144)
when we factorise this quadratic formula
(x² + 24x + 144)
= x² + 12x + 12x +144
= x ( x+ 12) + 12 (x + 12)
(x+12)(x+12)
the area of the square plot has been calculated by multiplying the lengths of the 2 sides. As its a square, all sides are equal
the length of one side = x+12
the dimensions are given in the form ax + b
from the length x + 12 , a = 1 and b=12
the perimeter of the park = 4 * length of one side
therefore perimeter = 4 * (x+12)
= 4x + 48 yards
next we are asked to find the perimeter when x = 10 yards
perimeter = 4*10 + 48 = 40 + 48 = 88 yards