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Free_Kalibri [48]
3 years ago
9

The two

Mathematics
1 answer:
taurus [48]3 years ago
5 0

Answer:

x = 5

Step-by-step explanation:

Sides of large triangle: 4x and 15

Corresponding sides of small triangle: 3x + 1 and 12

\dfrac{4x}{15} = \dfrac{3x + 1}{12}

60 \times \dfrac{4x}{15} = 60 \times \dfrac{3x + 1}{12}

16x = 15x + 5

x = 5

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Triangle abc is located on a coordinate plane angle c is at (1,2) the triangle is rotated counter clockwise 90° about the origin
sertanlavr [38]

After rotating a point C 90° counterclockwise about the origin the coordinates of C' would be (-2, 1)

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Step-by-step explanation:

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Rhombus ADEF is inscribed into a triangle ABC so that they share angle A and the vertex E lies on the side BC . What is the leng
Thepotemich [5.8K]

Answer:

Length of side of rhombus is x=\frac{ab}{a+b}  

Step-by-step explanation:

Given Rhombus ADEF is inscribed into a triangle ABC so that they share angle A and the vertex E lies on the side BC. We have to find the length of side of rhombus.

It is also given that AB=a and AC=b

Let side of rhombus is x.

In ΔCEF and ΔCBA

∠CEF=∠CBA        (∵Corresponding angles)

∠CFE=∠CAB        (∵Corresponding angles)

By AA similarity rule, ΔCEF~ΔCBA

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\frac{EF}{AB}=\frac{CF}{AC}

⇒ \frac{x}{a}=\frac{b-x}{b}

⇒ xb=ab-ax

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⇒ x=\frac{ab}{a+b}

Hence, length of side of rhombus is x=\frac{ab}{a+b}  

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