The lengths, in order, of four consecutive sides of an equiangular hexagon are 1, 7, 2 and 4 units, respectively. what is the su
m of the lengths of the two remaining sides?
1 answer:
Let ABCDEF be an equilanqular hexagon with consecutive sides 1,7,4,2, respectively. All angles of this hexagon are equal to 120° (because total anglea sum is 720°).
Draw lines: CG parallel to ED, PG and AH parallel to BC and EG parallel to CD. You obtain three parallelograms CGED, PGEF, ABCH and one trapezoid APGH.
Since CGED is parallelogram, CG=ED=2, GE=CD=4.
Since ABCH is parallelogram, AH=BC=7, AB+CH=1. Then GH=CG-CH=2-1=1.
Since PFEG is parallelogram, PF=EG=4, EF=PG. Let's find GP. APGH is equilateral trapezoid, then AP=GH=1 ahd thus FA=1+4=5 and GP=AH-0.5-0.5=7-0.5-0.5=6.
Answer: All sides have lengths 1,7,4,2,6,5, respectively.
Draw lines: CG parallel to ED, PG and AH parallel to BC and EG parallel to CD. You obtain three parallelograms CGED, PGEF, ABCH and one trapezoid APGH.
Since CGED is parallelogram, CG=ED=2, GE=CD=4.
Since ABCH is parallelogram, AH=BC=7, AB+CH=1. Then GH=CG-CH=2-1=1.
Since PFEG is parallelogram, PF=EG=4, EF=PG. Let's find GP. APGH is equilateral trapezoid, then AP=GH=1 ahd thus FA=1+4=5 and GP=AH-0.5-0.5=7-0.5-0.5=6.
Answer: All sides have lengths 1,7,4,2,6,5, respectively.
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Answer:
Faisal receives $241
Ahmed receives $482
Walid receives $723
Step-by-step explanation:
I am going to build a system of equations to solve this question.
We have that:
x is the amount that Faysal received.
y is the amount that Ahmed received.
z is the amount that Walid received.
Ahmed, Walid and Faisal made $1446 profit from selling used books.
This means that
Ahmed to receive double amount of Faisal
This means that
Walid to receive triple amount of Faisal.
This means that
So
Faisal receives $241
Ahmed receives $482
Walid receives $723