3 years ago

A rhombus has sides 10 cm long and an angle of 60°. Find the diagonals of the rhombus.

1 answer:

8 0

Check the picture below.

recall that in a rhombus the diagonals bisect each other at a right-angle, and that all sides are equal.

thus the longer diagonal is 2a long, and the shorter diagonal is 2b long.

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2 years ago

If triangle ABC is similar to triangle DEC, find the values of x and y.

Mumz [18]

The values are x=8 and y=35, if the given ΔABC and ΔDEC are equal, it is obtained by Pythagoras theorem.

Step-by-step explanation:

The given are,

From ΔABC,

AB= 6

BC= 10

AC = x

From ΔDEC,

CD= 28

DE= 21

CE = y

Step:1

Pythagoras theorem from ΔABC,

$BC^{2}=AB^{2} + AC^{2}$ ...............(1)

Substitute the values,

$10^{2}$ = $6^{2}$ + $AC^{2}$

100 = 36 + $AC^{2}$

$AC^{2}$ = 100 - 36

= 64

AC = $\sqrt{64}$

AC = 8

AC = x = 8

Step:2

Pythagoras theorem for ΔDEC,

$CE^{2} = CD^{2} + DE^{2}$ ................(2)

From the values,

$CE^{2}$ = $28^{2}$ + $21^{2}$

$CE^{2}$ = 784 + 441

= 1225

CE = $\sqrt{1225}$

CE = 35

CE = y = 35

Result:

The values are x=8 and y=35, if the given ΔABC and ΔDEC are equal.

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3 years ago