Question

A rectangle has a perimeter of 28 units, an area of 48 square units, and sides that are either horizontal or vertical. If one vertex is the point (-5,-7), and the origin is in the interior of the rectangle, find the vertex of the rectangle that is opposite is (-5,-7)

Answer 1

The answer to your question is (1, 1)

Explanation:

Area = 48 u²

Perimeter = 28 units

Formula

Area = base x height = b x h

Perimeter = 2 base+ 2 height = 2b + 2h

Solve equations

b x h = 48

2b + 2h = 28

b = 48/h

2(48/h) + 2h = 28

96/h + 2h = 28

96 + 2h² = 28h

2h² - 28h + 96 = 0

h² - 14h + 48 = 0 Factor this polynomial

(h - 8) (h - 6) = 0

h₁ = 8 h₂ = 6

Base b = 48/h

b₁ = 48/8 = 6

b₂ = 48/6 = 8

If height = 8

New vertex = (1, 1)

If height = 6

New vertex = (3, -1)

But, we know that the origin is inside the rectangle, so the answer is (1, 1)