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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)

Respuesta :

joseaaronlara

Answer:

The answer to your question is (1, 1)

Step-by-step 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)

             

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