Geometry

Find the dimensions of a rectangular solid for which the sum of all the edges is 76, the total surface area is 206 square units, and the volume is 165 cubic units.

  1. 👍 0
  2. 👎 0
  3. 👁 165
  1. let the length, the width and the height be
    a , b, and c respectively

    make a sketch to see that
    4a + 4b + 4c = 76 ---> a+b+c = 19
    or c = 19 - a - b
    2ab + 2ac + 2bc = 206 ---> ab + ac + bc = 103
    abc = 165
    or c = 165/(ab)

    19-a-b = 165/ab
    19ab - a^2 b - ab^2 = 165
    ab(19 - a^2 - b^2) = 165

    from ab+ac+bc=103
    c(a+b) = 103 - ab
    c = (103-ab)/(a+b)

    165/(ab) = (103-ab)/(a+b)
    165a + 165b = 103ab - a^2 b^2
    165(a+b) = ab(103 - ab)

    ok, going on a hunch that the numbers are whole numbers, let's look at abc = 165
    and 165 = 11x5x3 , all primes

    test for ab+bc +ac = 55 + 15 + 33 = 103
    a+b+c = 11+5+3 = 19

    well, that was a lucky hunch,
    the sides are 11 , 5, and 3

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    1. A gardener has 140 feet of fencing to fence in a rectangular vegetable garden. Find the dimensions of the largest area he can fence. Find the possible rectangular area he can enclose. 2. Suppose a farmer has a large piece of

  2. MATH

    Which solid figure has 5 faces, 5 vertices, and 8 edges. Triangular pyramid Rectangular pyramid Pentagonal pyramid*** Triangular prism

  3. Pre-calculus

    From a circular piece of metal sheet with diameter 20 cm, a rectangular piece with perimeter 28 cm is to be cut as shown. Find the dimensions of the rectangular piece.

  4. solid mensuration

    the base of a rectangular solid is 4 ft. long and 3 ft. wide. find the volume of the solid if its diagonal is square root of 41 ft. .

  1. Math

    Consider the right rectangular prism shown. The figure shows a right rectangular prism whose dimensions are 8.5 centimeters, 2.25 centimeters, and 5.75 centimeters ​List the numbers of faces, edges, and vertices of the

  2. algebera

    1) Identify the solid form by the given net. :Triangular Prism :Triangular Pyramid*** :Cone :Triangle 2) Name the solid according to it's description: The figure has two bases that are parallel congruent circles. :Cylinder***

  3. math

    A rectangular box has a volume of $4320$ cubic inches and a surface area of $1704$ square inches. The sum of the lengths of its $12$ edges is $208$ inches. What would be the volume of the box, in cubic inches, if its length, width

  4. math

    a. A rectangular pen is built with one side against a barn. 1200 m of fencing are used for the other three sides of the pen. What dimensions maximize the area of the​ pen? b. A rancher plans to make four identical and

  1. Calc

    A rectangular page is to contain 30 sqaure inches of print. The margins on each side are 1 inch. Find the dimensions of the page sucha that the least amount of paper is used. A farmer plans to fence a rectangular pasture adjacent

  2. Calculus

    A pyramid with height 2h and rectangular base with dimensions 3b and 6b. Find the volume V of this solid.

  3. Volume of a rectangular prism

    Hello, if the volume of a rectangular prism is LWH = 64 cubic inches, what are the dimensions of a rectangular prism with dimensions twice as long? Thank you!

  4. math

    A rectangular box has a volume of $4320$ cubic inches and a surface area of $1704$ square inches. The sum of the lengths of its $12$ edges is $208$ inches. What would be the volume of the box, in cubic inches, if its length, width

You can view more similar questions or ask a new question.