Question

A piece of sheet metal, $18$ inches wide, is bent to form the gutter shown in figure. If the cross-sectional area is $36$ square inches, find the depth of the gutter.

• A. $2$ inches
• B. $3$ inches
• C. $4$ inches
• D. $6$ inches

Answer 1

Answer: (B), (D)

The correct options are
B $3$ inches
D $6$ inches

Cross-sectional area $=(18-2x)x=36$
$-2x^2+18x=36$
$2x^2-18x+36=0$
$x^2-9x+18=0$
$x^2-(6+3)x+18=0$
$x(x-3)-6(x-3)=0$
$(x-6)(x-3)=0$
$x=3,6$