math

posted by .

The area of a rectangle is 24, and its diagonal is radical 52. Find its dimensions and perimeter.

Longer side = ?
Shorter side = ?
Perimeter = ?

  • math -

    Let the dimensions be a and b.
    ab = 24
    a^2 + b^2 = 52

    a^2 + (24/a)^2 = 52

    a^4 -52a^2 + 576 = 0
    (a^2 -36)(a^2 -16)
    a^2 = 36 or 16
    a = 6 or 4
    b = 4 or 6

  • math -

    Thank You!

  • math -

    Let X and Y represent the sides of
    the rectangle.

    X^2 + Y^2 = 52 = diagonal squared.
    XY = 24 =the area of rectangle.
    y = 24/X
    X^2 + (24/X)^2 = 52
    X^2 +576/X^2 = 52
    Multiply both sides by x^2 :
    X^4 + 576 = 52X^2
    X^4 - 52X^2 + 576 = 0. used computer to
    help find roots: X = -4, X = 4, X = -6,
    X = 6. Select the positive roots:
    The sides are 4 and 6. P = (2*4) +(2*6)
    = 20

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    Find the Maximum area for the given perimeter of a rectangle. State the length and width of the rectangle. 28 inches Well, finally a calculus problem. Ok, we know that the area for a rectangle is A=l*w and the perimeter is P=2(l+w) …
  2. Math

    Checking my son's homework and want to see if he figured this out correctly .. i am too old to be revisiting this math ... Here is the question ... The perimeter of a rectangle patio is six times the length of the shorter side. If …
  3. Pre-Cal

    The diagonal and the longer side of a rectangle make an angle of 43.2. If the longer side is 12.6cm, find the length of the shorter side.
  4. grade 6 math

    The shorter side of a rectangle is 20 m. Decreasing the longer side by 30 cm reduces the perimeter by one half. How long are the longer sides of the original rectangle?
  5. Math

    Abigail Adventuresome took a shortcut along the diagonal of a rectangular field and saved a distance equal to 1/3 the length of the longer side.Find the retio of the length of the shorter side of the rectangle to that of the longer …
  6. algabra 2

    One side of a triangle is 4 cm longer than the shortest side and 2 cm shorter than the longest side. The perimeter is 38 cm. Find the dimensions of the triangle.
  7. Geometry

    A rectangle has the same perimeter as a square. If the area of the rectangle is 9 less than the area of the square, the side length of the square is how much longer than the shorter side of the rectangle ?
  8. math

    A square has the same area as a rectangle whose longer side is 2 times the length of its shorter side. If the perimeter of the rectangle is 24, what is the perimeter of the square?
  9. geometryproblems

    one side of the triangular banner is 1 1/2 times longer than the second side and 2 cm. shorter than the third side. the perimeter of the triangle is 98 cm. how long is the shorter side?
  10. Geometry

    A diagonal of a square has the same length as a diagonal of a rectangle. The area of the rectangle is 60% of the area of the square. What is the ratio of the shorter side to the longer side of the rectangle?

More Similar Questions