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3 years ago

The side of rhombus is 14 in. The obtuse angle is 160º. Find the longer diagonal of the rhombus.

Mathematics

1 answer:

Mandarinka [93]3 years ago

3 0

Answer:

x = 27.57 in to the nearest hundredth.

Step-by-step explanation:

The longer diagonal is opposite the obtuse angle.

Also as it is a rhombus all sides = 14 in.

Use the Cosine Rule:

x^2 = 14^2 + 14^2 - 2*14^2 cos 160

x^2 = 760.36

x = sqrt 760.36

x = 27.57 in.

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Mariulka [41]

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Length = 10 ft

Width = 5 ft

Explanation

Area of the rectangle given = 50 ft²

Let the width of the rectangle be x

So this means the length of the rectangle will be 3x - 5

What to find:

The dimensions of the rectangle.

Step-by-step solution:

Area of a rectangle = length x width

i.e A = L x W

Put A = 50, L = 3x - 5, W = x into the formula.

$\begin{gathered} 50=(3x-5)x \\ 50=3x^2-5x \\ 3x^2-5x-50=0 \end{gathered}$

The quadratic equation can now be solve using factorization method:

$\begin{gathered} 3x^2-5x-50=0 \\ 3x^2-15x+10x-50=0 \\ 3x(x-5)+10(x-5)=0 \\ (3x+10)(x-5)=0 \\ 3x+10=0\text{ }or\text{ }x-5=0 \\ 3x=-10\text{ }or\text{ }x=5 \\ x=-\frac{10}{3}\text{ }or\text{ }x=5 \end{gathered}$

Since the dimension can not be negative, hence the value of x will be = 5.

Therefore, the dimensions of the rectangle will be:

$\begin{gathered} Length=3x-5=3(5)-5=15-5=10\text{ }ft \\ \\ Width=x=5\text{ }ft \end{gathered}$

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