SOLUTION: Please Help Rectangles ABCD and EFGH have equal areas. If EF= 1/2AB, which of the following is true...? (1) FG = 2BC (2) (AB)(GH) = (BC)(EH) (3) AB/EF = BC/FG (4) AB/BC = EF

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Please Help Rectangles ABCD and EFGH have equal areas. If EF= 1/2AB, which of the following is true...? (1) FG = 2BC (2) (AB)(GH) = (BC)(EH) (3) AB/EF = BC/FG (4) AB/BC = EF      Log On


   

Question 438441: Please Help
Rectangles ABCD and EFGH have equal areas. If EF= 1/2AB, which of the following is true...?
(1) FG = 2BC
(2) (AB)(GH) = (BC)(EH)
(3) AB/EF = BC/FG
(4) AB/BC = EF/FG
Found 2 solutions by MathLover1, Gogonati:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
Rectangles ABCD and EFGH have equal areas
EF=+1%2F2AB.....->...AB=+2EF
FG+=+2BC is true........if length of the rectangle ABCD is 2 times greater than length of the rectangles EFGH, then the width of the rectangles ABCD is also 2 times greater than length of the rectangle EFGH because they have equal areas

Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
Since EF=AB/2, then AB=2EF.
Area of ABCD=ABXBC and area of EFGH=EFXFG,since these two areas are equal we write:ABXBC=EFXFG, substitute on these equalities: AB=2EF and we get:
2EFXBC=EFXFG, divide both sides of equality by EF and get:
2BC=FG, this relation is true, thus the first answer is true.