Construct a trapezium ABCD such that AD is parallel to BC, AB = 4.8 cm, BC = 6.8 cm, CD = 5.4 cm and ∠ABC = 60°. Measure and wri
te down the length of AC.
1 answer:
Answer:
AC = 6.05 cm
Step-by-step explanation:
We can draw two different trapeziums with the information given.
The possible drawings of the trapezium ABCD are in the image attached.
In both trapeziums, the length of AC is the same, and we can calculate this length using the law of cosines in the triangle ABC:
AC^2 = AB^2 + BC^2 - 2 * AB * BC * cos(B)
AC^2 = 4.8^2 + 6.8^2 - 2 * 4.8 * 6.8 * cos(60)
AC^2 = 23.04 + 46.24 - 65.28 * 0.5
AC^2 = 36.64
AC = 6.05 cm
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The two containers hold 328 ounces at the they hold same amount of water.
<u>Step-by-step explanation:</u>
The equations below model the ounces of water, y, in each container after x minutes.
At the time after the start when the containers hold the same amount of water, the two equations must be equal.
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The first step is to divide everything by 2 to make it simplified.
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Now put everything on the left .
Add the like terms together to further reduce the equation
Factorizing the equation to find the roots of the equation.
Here, b = -12 and c = -28
where,
- b is the sum of the roots ⇒ -14 + 2 = -12
- c is the product of the roots ⇒ -14 × 2 = -28
- Therefore, (x-14) (x+2) = 0
- The solution is x = -2 or x = 14
Take x = 14 and substitute in any of the given two equations,
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⇒ 328 ounces
∴ The two containers hold 328 ounces at the they hold same amount of water.