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3 years ago

Is my answer correct??

Mathematics

1 answer:

Studentka2010 [4]3 years ago

3 0

Answer:

The correct answer is the first choice: Hinge Theorem.

Explanation:

The Hinge Theorem compares the lengths of two sides of two triangles, given that the other two pairs of sides are congruent and the included angles are different.

The theorem states that if two sides of a triangle are congruent to two sides of another triangle and the included angle of one triangle is greater than the included angle of the other triangle, then length of the third side of the first triangle is greater than the length of the third side of the second triangle.

The figures shows triangles UVT and STV

The angle UVT is greater than the angle STV.

The sides ST and VU are congruent, as the small vertical marks indicate.

The side TV is a common side of both triangles.

Then, you already have that two sides of the triangle STV are congruent to two sides of triangle UVT and the angle UVT is greater than the angle STV.

Hence, by the HInge Theorem the side TU is greater than side SV.

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4 years ago

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Read 2 more answers

A rhombus has a side length equal to one of the diagonals. The other diagonal is 4cm longer. Find the area of the rhombus.

klasskru [66]

Answer:

The area of the rhombus is 25.83 cm².

Step-by-step explanation:

The area of a rhombus is given by:

$A = \frac{d_{1} \times d_{2}}{2}$

Where:

d₁: is one diagonal

d₂: is the other diagonal = d₁ + 4 cm

We know that one side length of the rhombus is equal to d₁. We can imagine a right triangle inside the rhombus, with the following dimensions:

h: hypotenuse of the right triangle

a: one side of the right triangle

b: is the other side of the right triangle

From the above we know that:

h = d₁

$a = \frac{d_{2}}{2} = \frac{d_{1} + 4}{2}$

$b = \frac{d_{1}}{2}$

We can find d₁ with Pitagoras:

$h^{2} = a^{2} + b^{2}$

$d_{1}^{2} = (\frac{d_{1} + 4}{2})^{2} + (\frac{d_{1}}{2})^{2}$

$d_{1}^{2} = \frac{1}{4}(d_{1}^{2} + 8d_{1} + 16 + d_{1}^{2})$

By solving the above quadratic equation for d₁ and taking the positive solution we have:

$d_{1} = 5.46 cm$

So, d₂ is:

$d_{2} = d_{1} + 4 = 5.46 cm + 4 cm = 9.46 cm$

Now, we can find the area:

$A = \frac{d_{1} \times d_{2}}{2} = \frac{5.46 cm \times 9.46 cm}{2} = 25.83 cm^{2}$

Therefore, the area of the rhombus is 25.83 cm².

I hope it helps you!

3 0

3 years ago