SOLUTION: The cuboid has a width of 5cm and a length of 10cm and the surface area of 280cm� what is the height of the cuboid? I have found the answer on this website but i don't know how s

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Question 948504: The cuboid has a width of 5cm and a length of 10cm and the surface area of 280cm� what is the height of the cuboid?
I have found the answer on this website but i don't know how she got 30?
(http://www.algebra.com/algebra/homework/Surface-area/Surface-area.faq.question.857827.html)
It was answered by KMST(3526)
Found 2 solutions by macston, MathLover1:
Answer by macston(5194) (Show Source):
You can put this solution on YOUR website!
The surface area of each of two faces of the cuboid are A=L*W
A=L*W=5cm*10cm=50 sq cm
Since there are two this size (top and bottom), total area=2A=100 sq cm
The area of the sides is 280 sq cm- 100 sq cm=180 sq cm
The two ends of the cuboid that rise from the width each have area=(5cm)(h) and there are two of them:
(2)( 5 cm)(h)=(10cm)(h)
The two sides of the cuboid that rise from the length each have area=(10cm)(h) and there are two of them:
(2)(10 cm)(h)=(20cm)(h)
The sum of the area of the sides and ends:
(10 cm)(h)+(20 cm)(h)=(30 cm)h (30 cm is also the perimeter of the base)
This equals the remaining 180 sq cm of surface area:
(30 cm)h=180 sq cm Divide each side by 30 cm.
h=6 cm ANSWER: The height of the cuboid is 6 cm.

Answer by MathLover1(20850) (Show Source):
You can put this solution on YOUR website!

you are given:

find:= height of the cuboid, in cm
recall, the total surface area () of a cuboid is the sum of the areas of its faces (and all faces are rectangles) given by: