The width of a rectangle is represented by 5 + 2y the lingth is twice as long as the width. what is the perimeter of the rectangle? select all correct expressions

30+12y

Step-by-step explanation:

width=5+2y

length is twice its width

so 2(5+2y)=10+4y

perimeter=L+W+L+W

=2(L+W)

Therefore 2(5+2y+10+4y)

10+4y+20+8y

collect the like terms together

10+20+4y+8y

30+12y

so the answer=30+8y

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°