SOLUTION: Ref. Question 1048321: The lower square base of the Washington Monument has a side 21 ft. more than the upper square base. Area of the lower base is 1869 sq. ft. more than the u

Question 1048602: Ref. Question 1048321:
The lower square base of the Washington Monument has a side 21 ft. more than the upper square base. Area of the lower base is 1869 sq. ft. more than the upper base. Determine dimensions of each square.
Area = length * width
Let x = lower base
Let y = upper base

Lower:
Side: x + 21 Side: x + 21 Area: (x + 21) (x + 21)
Upper:
Side: y Side: y Area: y^2
y^2 = (x + 21) (x + 21) + 1869
y^2 = x^2 + 21x + 21x + 441 + 1869
y^2 = x^2 + 42x + 2310
Unsure from here.

(x + 21)^2 = x^2 + 1869
X^2 + 441 = X^2 + 1869
x^2 + 441 - 441 = X^2 + 1869 - 441
x^2 = x^2 + 1428
Stuck here.

" Answer:
(x + 21)^2 = x^2 + 1869
X^2 + 441 = X^2 + 1869 ******* (x+21)^2 = x^2 + 42x + 441
x^2 + 441 - 441 = X^2 + 1869 - 441
x^2 = x^2 + 1428 "

My attempt:
(x + 21)^2 = x^2 + 42x + 441 = x^2 + 1869
x^2 - x^2 + 42x + 441 - 441 = x^2 + 1869 - 441
42x = 1428
x = 34 (side of upper base)
34 + 21 = 55 (side of lower base)
34 * 34 = 1156 (area of upper)
55 * 55 = 3025 (area of lower)
3025 - 1156 = 1859
Where am I correct?

Found 4 solutions by advanced_Learner, solver91311, stanbon, MathLover1:
Answer by advanced_Learner(501)   (Show Source): You can put this solution on YOUR website!
The lower square base of the Washington Monument has a side 21 ft. more than the upper square base. Area of the lower base is 1869 sq. ft. more than the upper base. Determine dimensions of each square.

upper
side otherside } then area=xx=
lower otherside area=
=
=
= ,the upper side is and
,= is the side of the lower square base
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

The last part is correct:

"(x + 21)^2 = x^2 + 42x + 441 = x^2 + 1869
x^2 - x^2 + 42x + 441 - 441 = x^2 + 1869 - 441
42x = 1428
x = 34 (side of upper base)
34 + 21 = 55 (side of lower base)
34 * 34 = 1156 (area of upper)
55 * 55 = 3025 (area of lower)
3025 - 1156 = 1859"

John

My calculator said it, I believe it, that settles it

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
The lower square base of the Washington Monument has a side 21 ft. more than the upper square base. Area of the lower base is 1869 sq. ft. more than the upper base. Determine dimensions of each square.
Area = length * width
Let x = lower base
Let y = upper base
Lower:
Side: x + 21 Side: x + 21 Area: (x + 21) (x + 21)
Upper:
Side: x Side: x Area: x^2
----
Lower = Upper + 1869
(x+21)^2 = x^2 + 1869
x^2 + 42x + 441 = x^2 + 1869
42x = 1428
x = 34 ft.
etc.
----
Cheers,
Stan H.
------------
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

let the upper square base side be
if the lower square base of the Washington Monument has a side ft more than the upper square base , then the lower square base side is
if the rea of the lower base () is sq. ft. more than the upper base (), we have
.....solve for

now we know that the upper square base side is
then then the lower square base side is

check the areas:
lower base

uper base

check the difference:

which confirms our solutions

RELATED QUESTIONS
The lower square base of the Washington Monument has a side 21 ft. more than the upper... (answered by solver91311)
The height of the Washington monument is 50.5 inches more than 10 times the length of a... (answered by edjones)
If the height of the Washington Monument is 50.5 inches more than 10 times the length of... (answered by ankor@dixie-net.com)
The height of the Washington Monument is 50.5 inches more than 10 times the length of a... (answered by lynnlo)
cleopatra's needle consists of a frustum of a pyramid surmounted by a pyramid. the... (answered by solve_for_x)
Ref. Questions 1048321, 1048398: (x + 21)^2 = x^2 + 42x + 441 = x^2 + 1869 x^2 - x^2 (answered by Alan3354)
help please! a trapezoid has an area of 185d^2 sq. meters and a height of 15d meters.... (answered by amoresroy,robertb)
Find the total area of the frustum of a regular square pyramid which is inscribed in the (answered by ikleyn)
what is the area in square meters, of the base of the monument of a right square... (answered by Alan3354)