Cuboid

The sum of the lengths of the three edges of the cuboid that originate from one vertex is 210 cm. Edge length ratio is 7: 5: 3. Calculate the length of the edges.

Correct answer:

a =  98 cm
b =  70 cm
c =  42 cm

Step-by-step explanation:

$$\begin{gathered} s=a+b+c \\ s=210\text{ cm } \\ a:b:c=7:5:3 \\ k=s\mathrm{/}(7+5+3)=210\mathrm{/}(7+5+3)=14\text{ cm } \\ a=7\cdot k=7\cdot 14=98\text{ cm} \end{gathered}$$

$b=5\cdot k=5\cdot 14=70\text{ cm}$

$c=3\cdot k=3\cdot 14=42\text{ cm}$

Try another example

Related math problems and questions:

• Cuboid and ratio
  Find the dimensions of a cuboid having a volume of 810 cm³ if the lengths of its edges coming from the same vertex are in ratio 2: 3: 5
• Cuboid face diagonals
  The lengths of the cuboid edges are in the ratio 1: 2: 3. Will the lengths of its diagonals be the same ratio? The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid.
• Cuboid - edges
  The cuboid has dimensions in ratio 4: 3: 5, the shortest edge is 12 cm long. Find: (A) the lengths of the remaining edges, (B) the surface of the cuboid, (C) the volume of the cuboid
• Cuboid edges
  The lengths of the cuboid edges are in the ratio 2: 3: 4. Find their length if you know that the surface of the cuboid is 468 m².
• Cuboid edges
  Calculate the volume and surface of a cuboid whose edge lengths are in the ratio 2: 3: 4 and the longest edge measures 10cm.
• Cuboid edges in ratio
  Cuboid edges lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm³.
• Cube 7
  Calculate the volume of a cube, whose sum of the lengths of all edges is 276 cm.
• Cuboid - ratios
  The sizes of the edges of the cuboid are in the ratio 2: 3: 5. The smallest wall has an area of 54 cm². Calculate the surface area and volume of this cuboid.
• Ratio of edges
  The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.
• Prism
  Three cubes are glued into a prism. The sum of the lengths of all its edges is 115 cm. What is the length of one edge of the original cube?
• Edges or sides
  Calculate the cube volume, if the sum of the lengths of all sides is 276 cm.
• The block
  The block, the edges formed by three consecutive GP members, has a surface area of 112 cm². The sum of the edges that pass through one vertex is 14 cm. Calculate the volume of this block.
• Similar triangles
  The triangles ABC and XYZ are similar. Find the missing lengths of the sides of the triangles. a) a = 5 cm b = 8 cm x = 7.5 cm z = 9 cm b) a = 9 cm c = 12 cm y = 10 cm z = 8 cm c) b = 4 cm c = 8 cm x = 4.5 cm z = 6 cm
• Sum of the edges
  The sum of the lengths of all edges of the cube is 72 cm. How many cm² of colored paper are we going to use for sticking?
• Ratio-cuboid
  The lengths of the edges of the cuboid are in the ratio 2: 3: 6. Its body diagonal is 14 cm long. Calculate the volume and surface area of the cuboid.
• Cube edges
  The sum of the lengths of the cube edges is 42 cm. Calculate the surface of the cube.
• Right triangle - ratio
  The lengths of the legs of the right triangle ABC are in ratio b = 2: 3. The hypotenuse is 10 cm long. Calculate the lengths of the legs of that triangle.