2 years ago

Write an equation or inequality to represent the scenario:

Mathematics

1 answer:

aniked [119]2 years ago

6 0

<h3>The value of x is equal to 1.</h3><h3>6(x + 2) = 20x - 2</h3>

Distributive property.

6x + 12 = 20x - 2

Add 2 to both sides.

6x + 14 = 20x

Subtract 16x from both sides.

14 = 14x

Divide both sides by x.

x = 1

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Since BC is parallel to DE, triangles ABC and ADE are similar. What are the lengths of the unknown sides?

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Answer:

Option D. AC= 10 cm and CE= 5 cm

Step-by-step explanation:

From the given figure two triangles ΔABC and ΔADE are similar and two lines BC║DE.

From these similar triangles we know

$\frac{AB}{AD}=\frac{BC}{DE}=\frac{AC}{AE}$

$\frac{8}{12}=\frac{BC}{9}=\frac{AC}{AE}$

Therefore $\frac{AC}{AE}=\frac{8}{12}=\frac{2}{3}$

Or AC= $\frac{2}{3}AE$

Now from pythagoras theorem

AE = √(AD²+ED²) = √(12²+9²) = √(144+81) =√225 = 15 cm

Since we know side AC = $\frac{2}{3}AE$

= $\frac{2}{3}\times 15$

= 10 cm

Therefore AC = 10 cm and AE = 15cm and CE = (15-10) = 5 cm

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