A monument consists of two cubical blocks of granite, the smaller resting on the larger. The total height of the monument is 5 feet, and the area of the exposed surface is 61 square feet. Find the dimensions of the blocks.

Help please>.< Thank you in advance!

length of side of the larger --- x

length of side of the smaller -- y

x+y = 5

So what do we see?
We see 4 side faces of the larger = 4x^2
we see 4 side faces of the smaller = 4y^2
If we look straight down, we see a small face on top of the large face exposing the edge of the large face not covered by the smaller cube.
But isn't that just equal to the surface area of the large top?

so 5x^2 + 4y^2 = 61
from x+y=5 ---> y = 5-x
5x^2 + 4(25-10x+x^2) = 61
5x^2 + 100 - 40x + 4x^2 = 61
9x^2 -40x + 39=0
(x-3)(9x-13) = 0
x = 3 or x = 13/9

the blocks could be 3ft for the larger, and 2 ft on each side for the smaller
or
the larger be have a side of 32/9 and the smaller 13/9 ft

can you provide a check for the answers?

To find the dimensions of the blocks, we need to make some assumptions and use some mathematical reasoning. Let's assume the following:

Let the length, width, and height of the smaller cubical block be denoted by "x."
Since it is resting on the larger block, the length, width, and height of the larger cubical block will be "2x" since it is twice as long, wide, and tall as the smaller block.

Now, let's calculate the total surface area of the monument.

The surface area of the smaller block can be calculated by:
- The top and bottom faces have an area of x * x = x^2.
- The four side faces each have an area of x * x = x^2.
So, the surface area of the smaller block is 2 * (x^2) + 4 * (x^2) = 6 * (x^2).

The surface area of the larger block can be calculated by:
- The top and bottom faces have an area of (2x) * (2x) = 4x^2.
- The four side faces each have an area of 2x * (2x) = 4x^2.
So, the surface area of the larger block is 2 * (4x^2) + 4 * (4x^2) = 20 * (x^2).

The total surface area of the monument is given as 61 square feet. Therefore, we have the equation:

Total surface area = Surface area of smaller block + Surface area of larger block
61 = 6 * (x^2) + 20 * (x^2)

Simplifying the equation:
61 = 26 * (x^2)

Dividing both sides by 26:
x^2 = 61 / 26

Taking the square root of both sides:
x = √(61 / 26)

Now, we can calculate the value of x:
x ≈ 1.48

So, the dimensions of the smaller block are approximately 1.48 feet.

Therefore, the dimensions of the larger block can be found by multiplying the dimensions of the smaller block by 2:
Length = 2 * x ≈ 2 * 1.48 = 2.96 feet
Width = 2 * x ≈ 2 * 1.48 = 2.96 feet
Height = 2 * x ≈ 2 * 1.48 = 2.96 feet

Hence, the dimensions of the smaller block are approximately 1.48 feet, and the dimensions of the larger block are approximately 2.96 feet by 2.96 feet by 2.96 feet.