The surface area of the rectangular prism below is 286in2. Find the height.

1 answer:

Rudiy273 years ago

4 0

Answer: $7in$

Step-by-step explanation:

$Formula: A=2(wl+hl+hw)$

Solve for h;

Let's begin by dividing by 2.

$\frac{A}{2}=wl+hl+hw$

Subtract wl because it's the only term that doesn't have h.

$\frac{A}{2}-wl=hl+hw$

Plug your values into the formula.

$\frac{286in^2}{2}-(5in)(9in) =h(9in)+h(5in)\\143in^2-45in^2=9inh+5inh\\98in^2=14inh$

Divide by 14 to isolate h.

$\frac{98in^2}{14in}=h$

$7in=h$

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Katen [24]

Answer:

a°=135°

b°=35°

c°=85°

d°=67°

Step-by-step explanation:

113×2=226

226–91=135

95×2=190

190–91=99

360–(226+99)=35

35+135=170

170÷2=85°

35+99=134°

134÷2=67°

3 0

3 years ago

DanielleElmas [232]

Answer:

135 degrees

Step-by-step explanation:

Angle CBD is the sum of angle ABC and angle ABD, so we find these first
An Isosceles triangle has 2 equal sides and 2 equal angles
Isosceles triangle theorem tells us that the 2 equal angles are respectively opposite the equal sides
Since triangle ABC has sides AB=AC, then angle ACB = angle ABC
So knowing that angles of triangle add up to 180, then
$\angle CAB+\angle ACB+\angle ABC=180\\(50)+\angle ACB+\angle ABC=180\\50-(50)+\angle ACB+\angle ABC=180-(50)\\\angle ACB+\angle ABC=130\\But,\angle ACB=\angle ABC,so\\(\angle ABC)+\angle ABC=130\\2\angle ABC=130\\\angle ABC=65$
Now we do the next triangle to get ABD
Since triangle ABD has sides AB=BD, then angle BDA = angle BAD
So knowing that angles of triangle add up to 180, then
$\angle BDA+\angle BAD+\angle ABD=180\\(55)+\angle BAD+\angle ABD=180\\But,\angle BDA=\angle BAD,so\\(55)+(55)+\angle ABD=180\\110+\angle ABD=180\\110-(110)+\angle ABD=180-(110)\\\angle ABD=70$
Now we said, angle CBD is the sum of angle ABC and angle ABD, so
$\angle ABC+\angle ABD=\angle CBD\\(65)+(70)=\angle CBD\\\angle CBD=135$