Investigating Rectangles, Rhombi, and Squares? Geometry Help?

Question

If the diagonals of a rhombus are 10 cm and 24 cm, then the length of each side of the rhombus is 26 cm.

Sometimes

Always

Never

POINT VALUE: 1 points

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In rhombus ABCD, the diagonals intersect at point E. If the measure of angle ABC = 84 degrees and AC = 18 cm, find the length of each side of the rhombus to the nearest tenth. (Hint: Draw and label a picture.)

12.1 cm

13.5 cm

18.1 cm

26.9 cm

POINT VALUE: 3 points

do your best to not necessarily answer, but explain the process for both

Answer 1

First question: Never. In fact, the length of each side is 13 cm, because the diagonals divide the rhombus into four right triangles with legs of 5 and 12 cm, and the sides are the hypotenuses (or is that hypotenusi?) [Y!A spell checker accepted "hypotenuses" there.]

Second question: 13.5 cm

Again, the diagonals (which include segment AC) divide the rhombus into four right triangles. Angle ABC is bisected by diagonal BD, and angle DBC (measuring 42 degrees) is the angle opposite the half-diagonal EC (length: 9cm).

The sine of a 42-degree angle is therefore the ratio of 9cm to the side:

sin(42°) = 9cm / s, so

s = 9cm / sin(42°) = 9cm / 0.669 = 13.5cm (to the nearest tenth)

Answer 2

never. one of the diaganals has to be longer than a side.

triangle ABE. B is 42(half of 84) side b is 9(half of 18) and angle E is 90

then use law of sines sinA/a=sinB/b=sinC/c

sin(90)/x=sin(42)/9

1/x=.0743

x=13.5cm

make it a good day