Answer:
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1/6d + 2/3 = 1/4(d - 2)
First, simplify
![\frac{1}{6} d](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B6%7D%20d)
to
![\frac{d}{6}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bd%7D%7B6%7D%20)
/ Your problem should look like:
![\frac{d}{6}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bd%7D%7B6%7D%20)
+
![\frac{2}{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%7D%7B3%7D%20)
=
![\frac{1}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B4%7D%20)
(d - 2)
Second, simplify
![\frac{1}{4} (d - 2)](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B4%7D%20%28d%20-%202%29)
to
![\frac{d-2}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bd-2%7D%7B4%7D%20)
/ Your problem should look like:
![\frac{d}{6}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bd%7D%7B6%7D%20)
+
![\frac{2}{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%7D%7B3%7D%20)
=
Third, multiply both sides by 12 (the LCM of 6,4) / Your problem should look like: 2d + 8 = 3(d - 2)
Fourth, expand. / Your problem should look like: 2d + 8 = 3d - 6
Fifth, subtract 2d from both sides. / Your problem should look like: 8 = 3d - 6 - 2d
Sixth, simplify 3d - 6 - 2d to d - 6 / Your problem should look like: 8 = d - 6
Seventh,add 6 to both sides. / Your problem should look like: 8 + 6 = d
Eighth, simplify 8 + 6 to 14 / Your problem should look like:14 = d
Ninth, switch sides. / Your problem should look like: d = 14
Answer:
d = 14
Answer:
The distance between 12m-sides is
.
Step-by-step explanation:
It is given that the parallelogram has sides 10m and 12m and an angle of 45°.
Draw an altitude from one 12m side to another 12 m side as shown in below figure.
The opposite angles of parallelogram are same. Two angles are obtuse angles and two are acute angle.
Since angle C is acute angle therefore it must be 45 degree.
![\sin\theta=\frac{perpendicular}{hypotenuse}](https://tex.z-dn.net/?f=%5Csin%5Ctheta%3D%5Cfrac%7Bperpendicular%7D%7Bhypotenuse%7D)
![\sin C=\frac{BE}{BC}](https://tex.z-dn.net/?f=%5Csin%20C%3D%5Cfrac%7BBE%7D%7BBC%7D)
![\sin(45^{\circ})=\frac{d}{10}](https://tex.z-dn.net/?f=%5Csin%2845%5E%7B%5Ccirc%7D%29%3D%5Cfrac%7Bd%7D%7B10%7D)
![\frac{1}{\sqrt{2}}=\frac{d}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%3D%5Cfrac%7Bd%7D%7B10%7D)
![\frac{10}{\sqrt{2}}=d](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7B%5Csqrt%7B2%7D%7D%3Dd)
![\frac{10}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}=d](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7B%5Csqrt%7B2%7D%7D%5Ctimes%20%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%7B2%7D%7D%3Dd)
![\frac{10\sqrt{2}}{2}=d](https://tex.z-dn.net/?f=%5Cfrac%7B10%5Csqrt%7B2%7D%7D%7B2%7D%3Dd)
![5\sqrt{2}=d](https://tex.z-dn.net/?f=5%5Csqrt%7B2%7D%3Dd)
Therefore the distance between 12m-sides is
.
2L + 2W = 116
L = 2W + 10
2(2W+10) + 2W = 6W + 20 = 116
6W = 96
W = 16
L = 2W + 10
L = 2(16) + 10 = 32 + 10 = <u><em>42 cm</em></u>