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In the figure above AB = BC = CD = 5 units and AD = 13 units
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16 Jun 2023, 00:55
16 Jun 2023, 00:55
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In the figure above AB = BC = CD = 5 units and AD = 13 units
Quantity A |
Quantity B |
Area of BCEF |
15 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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Re: In the figure above AB = BC = CD = 5 units and AD = 13 units
[#permalink]
15 Jul 2023, 13:23
15 Jul 2023, 13:23
Expert Reply
OE
Consider rectangle BCEF,
Since BC = EF, that implies EF = 5 units.
As AB = CD, we can say AF = ED,
As EF = 5, AF = ED and AD = 13, we can say AF = ED = 4 units.
Consider right angled triangles AFB and DEC,
AF = ED = 4,
AB = CD = 5,
Hence, BF = CE = 3 units.
Area of Rectangle BCEF 15
= Length × Breadth
= BF × EF
= 3 × 5
= 15
So A is 15 and B is 15
C is the answer
Consider rectangle BCEF,
Since BC = EF, that implies EF = 5 units.
As AB = CD, we can say AF = ED,
As EF = 5, AF = ED and AD = 13, we can say AF = ED = 4 units.
Consider right angled triangles AFB and DEC,
AF = ED = 4,
AB = CD = 5,
Hence, BF = CE = 3 units.
Area of Rectangle BCEF 15
= Length × Breadth
= BF × EF
= 3 × 5
= 15
So A is 15 and B is 15
C is the answer
Re: In the figure above AB = BC = CD = 5 units and AD = 13 units
[#permalink]
16 Jul 2023, 02:48
16 Jul 2023, 02:48
1
In the figure AD = AF + FE + ED
Since the line BF & CE are perpendicular to AD, FE = 5 units
Therefore AF + ED = 8 units
BF = CE, since the lines are perpendicular to each other.
AB = 5 units;
Using pythogorean triplets
AF = 3 units ; BF = 4 units (or)
AF = 4 units ; BF = 3 units
Since AF+ED = 8 units;
AF = 4 units & BF = 3 units
Area(BCEF) = 5 x 3 = 15 sq units
Hence, option C
Since the line BF & CE are perpendicular to AD, FE = 5 units
Therefore AF + ED = 8 units
BF = CE, since the lines are perpendicular to each other.
AB = 5 units;
Using pythogorean triplets
AF = 3 units ; BF = 4 units (or)
AF = 4 units ; BF = 3 units
Since AF+ED = 8 units;
AF = 4 units & BF = 3 units
Area(BCEF) = 5 x 3 = 15 sq units
Hence, option C
