Question

Please help. Find the dimensions of a rectangle that has a perimeter of 16cm and area of 13 cm^2

Answer 1

still here ~

Answer 2

1) P = 2b + 2h = 16
2) A = b*h = 13
From eq. (1): b = 8 - h
isolate in eq. (2) : (8 - h)(h) = 13
8h - h^2 = 13
h^2 - 8h + 13 = 0
using quadratic formula: \[(-b +/- \sqrt{b^2 - 4ac}) / 2a\]
h = 4 +/- sqrt(3)
so assume h = 4+ sqrt(3)
using eq. (1): b = 8 - (4+sqrt(3))
b = 4 - sqrt(3)

this can be verified in eq. (2)
also, the assumption of h = 4 + sqrt(3) instead of 4 - sqrt(3) was arbitrary, the dimensions will be the same independent of this assumption

so the dimentions are 4 + sqrt(3), 4 - sqrt(3)