Problem Solving

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.



So, we can add our lengths as follows.


From here, if we focus on one of the 4 right triangles....

...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