Question

A piece of sheet metal is 24 inches wide the cross section is 54 what is the depth

Answer 1

Answer:

Width = 18, height = 3

Or

Width = 6, height = 9

Step-by-step explanation:

Complete question

( A piece of sheet metal 24 inches wide is bent to form a gutter as shown in the picture below, if the cross sectional area is 54 square inches, find the depth of the gutter).

X = width, Y = height

X - 2y = 24........ equation i

X = 24 - 2y.......... equation ii

Area = xy

54 = xy........ equation iii

Put equation ii into equation iii

54 = (24 - 2y) * y

54 = 24y - 2y²

2y² - 24y + 54 = 0........ equation iv

Solving equation iv using quadratic methods,

Factors = (y-3), (y-9)

(Y-3)(y-9) = 0

y = 3 or y = 9

Substitute y = 3 or y = 9 into equation ii

X = 24 -2(3) = 18 or x = 24 - 2(9) = 6

If Width = 18, height = 3

Or

Width = 6, height = 9