MATH ALGEBRA GRADE SEVEN

Question

A statue is to be placed in the center of the park. The area of the base of the statue is 4x^(2)+12x+9m^(2). Find the lengths of the sides of the statue, if x=4 meters.

Answer 1

Area = 4x^2 + 12x + 9m^2

= 4(2)^2 + 12(2) + 9m^2

= 16 + 24 + 9m^2

= 40 + 9m^2

If the base is a sqare then the sides are the square root of the area

sides = sqr(40+9m^2) meters

each side would then be a minimum sqr40 = about 6.32 meters

if m = 1 then each side would = 7 meters

if m = 3, then each side would = 11 meters

4x^2 +12x + 9m^2 would be a perfect square if the middle term had been 12xm

4x^2 +12xm + 9m^2

= (4x +3m)^2

then each side of a square would be 4x +3m

with x= 2

then each side = 8+3m

minimum side would then be 8 metres

if m=1, then each side = 11 metres

if m=2 each side = 14 metres

if m=3 each side = 17 metres

it's possible that middle term is a typo or the m got left out in the original problem. Otherwise it's a strange coincidence the trinomial came so close to being a perfect square

if it's not a square, if it's a rectangular base with the sides not equal, each side could theoretically be any value

Although as a realistic matter, the size of a park limits the size of the base of the statue.