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Savatey [412]
3 years ago
6

robin needed 3 2/3 feet of thread to finish a pillow she was making. if she has 2 times as much thread as she needs, what is the

length of the thread she has?
Mathematics
2 answers:
igor_vitrenko [27]3 years ago
5 0
7 1/3

3 2/3+3 2/3=7 1/3
coldgirl [10]3 years ago
4 0

Answer:

7\frac{1}{3} feet.

Step-by-step explanation:

We have been given that Robin needed 3 2/3 feet of thread to finish a pillow she was making. We are asked to find the length of thread, if she has 2 times as much as thread as she needs.

First of all, we will convert 3\frac{2}{3} into improper fraction as:

3\frac{2}{3}\rightarrow \frac{3*3+2}{3}=\frac{9+2}{3}=\frac{11}{3}

Two times the length of thread would be:

2\times\frac{11}{3}

\frac{2\times11}{3}

\frac{22}{3}

\frac{3*7+1}{3}

7\frac{1}{3}

Therefore, Robin had 7\frac{1}{3} feet of thread.

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Since the triangle is equilateral, all its angles are equal to 60°

AO is the bisector⇒∠OAD = 30°

AO AO is the hypotenuse, ∠OAD = 30°⇒

OD=10:2=5ft

By the Pythagorean theorem

10^2=AD^2+5^2\\AD=\sqrt{100-25} \\AD=\sqrt{75}

AC=AD+DC=2\sqrt{75}=10\sqrt{3}

S=\frac{a^2\sqrt{3} }{4}

S=\frac{(10\sqrt{3})^2\sqrt{3}  }{4} =\frac{300\sqrt{3} }{4} =75\sqrt{3} ft^2

Answer: A) S=75\sqrt{3}ft²

P.S. Hello from Russia and sorry for my bad english :^)

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