The surface area of a box is 160 square inches. The length of the box is twice its width, and is 4 inches less than its height. What is the height of the box, in inches?

the height of the box is 9 inches

solution given:

total surface area of a box=160 square inches

let length, width, and height be l,b, and h respectively.

according to the question:

l=2b

∴b =

l=h-4

∴ h=l+4

we have

total surface area of a box=160 square inches

2(lb+lh+bh)=160

doing middle term factorization

taking common from each two terms

l(l+8)-5(l+8)=0

(l+8)(l-5)=0

either

l=-8[neglected as length is always positive]

or

l=5

now

b=

h=5+4=9

Step-by-step explanation:

step-by-step explanation:

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180