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In the rhombus ABCD, the length of diagonal BD is 6 and the

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by AAPL » Fri Nov 16, 2018 4:43 am
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In the rhombus ABCD, the length of diagonal BD is 6 and the length of diagonal AC is 8. What is the perimeter of ABCD?

A. 10
B. 14
C. 20
D. 24
E. 28

OA C.
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by Brent@GMATPrepNow » Fri Nov 16, 2018 6:34 am
AAPL wrote:Manhattan Prep

In the rhombus ABCD, the length of diagonal BD is 6 and the length of diagonal AC is 8. What is the perimeter of ABCD?

A. 10
B. 14
C. 20
D. 24
E. 28

OA C.
In a rhombus, the diagonals are perpendicular bisectors.
Image


So, we can add our lengths as follows.
Image

From here, if we focus on one of the 4 right triangles....
Image
...we see we can apply the Pythagorean Theorem to write: 3² + 4² = x²
Evaluate: 9 + 16 = x²
So, 25 = x²
Solve to get: x = 5

Since all 4 sides of a rhombus have equal length, the perimeter = (4)(5) = 20

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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