a rectangular solid has a volume of 640 cubic units. the width is 3 units more than the height and the length is 1 unit more than three times the height. find the dimensions of the solid.

v = lwh = (h+3)(3h+1)h = 640

h=5

so, the brick is 8 x 16 x 5

Paano nakuha ung 5?

To find the dimensions of the rectangular solid, we can use algebraic expressions based on the given information.

Let's assume the height of the solid is 'h' units.

According to the problem, the width is 3 units more than the height, so the width would be (h + 3) units.

Similarly, the length is 1 unit more than three times the height, so the length would be (3h + 1) units.

The volume of a rectangular solid can be calculated by multiplying its length, width, and height. Therefore, we have:

Volume = Length × Width × Height
640 = (3h + 1) × (h + 3) × h

Now, let's solve this equation to find the value of 'h.'

640 = (3h + 1) × (h + 3) × h
640 = (3h^2 + 10h + 3) × h
640 = 3h^3 + 10h^2 + 3h

To solve this equation, we can rearrange it to form a cubic equation:

3h^3 + 10h^2 + 3h - 640 = 0

To find the solution to this equation, we can use numerical methods or technology such as a graphing calculator.

Plugging the equation into a graphing calculator or using numerical methods, we find that one solution is approximately h ≈ 6.7.

Now, we can substitute this value back into the expressions for width and length to find the final dimensions:

Width = h + 3 = 6.7 + 3 = 9.7 units
Length = 3h + 1 = 3(6.7) + 1 = 20.1 + 1 = 21.1 units

Therefore, the dimensions of the rectangular solid are approximately:
Height ≈ 6.7 units
Width ≈ 9.7 units
Length ≈ 21.1 units