One side of a rectangle is 10 feet shorter than twice another side. find the length of the shorter side if we also know the perimeter of the rectangle is 28 feet.

  6 feet

Step-by-step explanation:

Let x represent the length of "another side." Then "one side" is ...

  2x -10 . . . . . . 10 feet shorter than twice another side

The sum of these two side lengths is half the perimeter, so is ...

  x + (2x -10) = 14 . . . . . two sides are half the perimeter

  3x = 24 . . . . . . . . . . . . add 10, collect terms

  x = 8 . . . . . . . . . . . . . . .divide by the coefficient of x

  (2x -10) = 2·8 -10 = 6 . . . . find "one side"

We have found "one side" to be 6 feet long, and "another side" to be 8 feet long. The shorter side is 6 feet.

468

step-by-step explanation:

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°