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

Question

Mathematics

Gwendolyn

20 July, 04:32

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

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Skylar House · 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