Triangles ABC and CDE are mathematically similar. a) Work out the length of DE.
b) Work out the length of AB.

From the given information in the diagram

a) The length of DE is 15cm and

b) The length of AB is 6cm

From the question,

Triangles ABC and CDE are mathematically similar.

a) To determine the length of DE

Since ΔABC is similar to ΔCDE

By similar triangles theorem, we can write that

From the diagram

/BC/ = 5cm

/CA/ = 8cm

/EC/ = 24 cm

/DE/ = ?

Putting these values into

We get

∴

Now, divide both sides by 8

/DE/ = 15cm

b) To work out the length of AB

Also, by similar triangles theorem, we can write that

From the diagram

/AB/ = ?

/CD/ = 18cm

/CA/ = 8cm

/EC/ = 24 cm

Putting these values into

We get

Now, multiply both sides by 18, that is

/AB/ = 6cm

Hence,

a) The length of DE is 15cm and

b) The length of AB is 6cm

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Step-by-step explanation:

The trick here is to notice that :

Now let's replace by the values we khow :

So AB=6 cm and DE=15 cm

the answer is b.)

< 1=< 2

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.