A monument consists of two cubical blocks of limestone. The smaller block rests on the larger. The total height of the monument is 5 m and the area of exposed surface is 61 m^2 . Determine the dimensions of the blocks.
+130516 Let H be the height of the larger monument and 5 - H be the height of the smaller.
The exposed surface area of the larger monument is 4H^2 + [H^2 - ( 5-H)^2] and the exposed surface area of the smaller monument is 5(5-H)^2
And setting this equal to the tottal exposed area, we have
4H^2 + [H^2 -( 5-H)^2] + 5(5-H)^2 = 61
5H^2 + 4(5 - H)^2 = 61
5H^2 + 4(H^2 - 10H + 25) = 61
5H^2 + 4H^2 - 40H + 39 = 0
9H^2 - 40H + 39 = 0 factor if possible
(9H - 13)(H - 3) = 0 ...so....the possible solutions are H = 13/9 and H = 3......but, since H is larger than 5 - H, the larger monument must have a side of 3 m and the smaller monument must have an edge of 5 - H = 5 - 3 = 2m
+130516 Let H be the height of the larger monument and 5 - H be the height of the smaller.
The exposed surface area of the larger monument is 4H^2 + [H^2 - ( 5-H)^2] and the exposed surface area of the smaller monument is 5(5-H)^2
And setting this equal to the tottal exposed area, we have
4H^2 + [H^2 -( 5-H)^2] + 5(5-H)^2 = 61
5H^2 + 4(5 - H)^2 = 61
5H^2 + 4(H^2 - 10H + 25) = 61
5H^2 + 4H^2 - 40H + 39 = 0
9H^2 - 40H + 39 = 0 factor if possible
(9H - 13)(H - 3) = 0 ...so....the possible solutions are H = 13/9 and H = 3......but, since H is larger than 5 - H, the larger monument must have a side of 3 m and the smaller monument must have an edge of 5 - H = 5 - 3 = 2m
