Question

melinda is using a rectangular brass bar in a sculpture she is creating. the brass bar has a length that is 4 more than 3 times its width if the area of the rectangular brass bar is 480 inches what are the dimensions answer

Answer 1

Answer:

The dimension of Length = L

The dimension of width = L

The dimension of Area = L²

Explanation:

A dimension is one of the physical properties that are regarded as fundamental measures of a physical quantity, such as mass, length and time.

L - length , W - width , A- Area

A= W × L (Formula for Area)

Given:

L= 4 + 3W ( length that is 4 more than 3 times its width)

Area = 480 inches

A= W × L

Sub. Given into Formula of Area

480= W (4 + 3W)

480= 4W + 3W²

3W² + 4W - 480= 0

a=3 b=4 c= -480

where W = unknown using the quadratic equation

W= -b ± √ (b² - 4ac) / 2a

W= -4 ± √ (4² - 4.3.-480)/ 2.3

W= -4 ± √ (16 + 5760)/ 6

W= -4 ± √ (5776)/ 6

W = (-4 ± 76)/6

W = (-4 + 76)/6 or (-4-76)/6

W = 72/6 or -80/6

W = 12 or - 13.6

We choose w=12 inches

Sub. W into L

L= 4 + 3W

L= 4 + 3×12

L= 40 inches

Area= W × L

= 40 inches × 12 inches

Area = 480 inches ²

Dimension wise

The dimension of Length = L

The dimension of width = L

The dimension of Area = L²

Answer 2

Answer:

180 x 60 inches

Width = 60 inches

Length = 180 inches

Explanation:

Given

Let L = Length

W = Width

P = Perimeter

Length = 3 * Width

L = 3W

Perimeter of Brass = 480 inches

P = 480

Perimeter is given as 2(L + W);

So, 2 (L + W) = 480

L + W = 480/2

L + W = 240

Substitute 3W for L; so,

3W + W = 240

4W = 240

W = 240/4

W = 60 inches

L = 3W

L = 3 * 60

L = 180 inches