# math

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1. find the lateral area of a right prism whose altitude measures 20 cm and whose base is a square with a width 7 cm long.
2. the volume of a rectangular solid is 5376 cubic meters, and the base is 24 meters by 16 meters. find the height of the solid.
3. a rectangle has a perimeter of 22cm and an area of 30 cubic meter. what are its dimensions?

• math -

1. The lateral area is the sum of the
areas of the vertical sides.
Al = 2(W*h) + 2(L*h).
Al = 2( 7*20) + 2(7*20) = 560 cm^2.

2. V = L*W*h.
22*16*h = 5376.
Solve for h.

3. 2W + 2L = 22,
Divide both sides by 2:
L + W = 11,
L = 11-W.

L*W = 30,
Substitute 11-W for L:
(11-W)W = 30,
-W^2+11W-30 = 0,
W^2-11W+30 = 0,
(W-5)(w-6) = 0,
W = 5 or 6.

L+5 = 11,
L = 6.

Dimensions = 6 x 5.

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