Question

If each quadrilateral is a rhombus, find the missing measures
BC = 28 and BD = 32

Answer 1

Answer:

Step-by-step explanation:

CD = 28 (same as BC all sides are equal)

FD = 28 (same as BC all sides are equal)

BEF makes a right angled triangle

with 1side = 16, and hyp = 28

using pythagoras theorem

EF = 4 sqrt(33)

EC = 8 sqrt(33)

Answer 2

The answers are:

CD = 28cm

FD = 16 cm

EF = 23 cm

EC = 46 cm

Step-by-step explanation:

BCDE is a rhombus where $BC = 28 cm, and BD = 32 cm$

• BC is one of the sides of the rhombus, thus, all the sides (CD, DE, EB) will be 28 cm.

So, CD = 28cm

• Now, $BD = 32 cm,$ which is the diagonal of the rhombus.

The diagonals bisect each other at a 90-degree angle.

Hence, FD$= \frac{1}{2} \times BD = \frac{1}{2} \times32 cm = 16 cm$

So, FD = 16 cm

• To find EF, we can consider $\triangle EFD$, which is right-angled at F, $FD = 16 cm$ and $ED = 28 cm$.

Thus, from Pythagoras theorem,

$ED^2 = EF^2 + FD^2$

$28^2 = EF^2 + 16^2$

$EF^2 = 28^2 - 16^2$

$EF^2 = 784 - 256 = 528$

$EF = 22.97 =23 cm$

So, EF = 23 cm

• EC would be two times EF( since diagonals bisect each other)

Therefore, EC $= 2\times 23 = 46 cm$

So, EC = 46 cm