# Math

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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.

• Math -

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

• Math -

can you provide a check for the answers?

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