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BartSMP [9]
3 years ago
6

What is x given ABC~DBE. Show your work

Mathematics
1 answer:
alexandr1967 [171]3 years ago
5 0

x = 37.5 (or) \frac{75}{2}

Solution:

Given \triangle A B C \sim \triangle D B E

AC = 50, DE = 30, EC = 25, BE = x, BC = 25 + x

To find the value of x:

Property of similar triangles:

If two triangles are similar then the corresponding angles are congruent and the corresponding sides are in proportion.

$\frac{BE}{BC} =\frac{DE}{AC}

$\frac{x}{25+x} =\frac{30}{50}

Do cross multiplication, we get

50x=30(25+x)

50x=750+30x

Subtract 30x from both sides of the equation.

20x=750

Divide by 20 on both sides of the equation, we get

x = 37.5 (or) \frac{75}{2}

Hence the value of x is 37.5 or \frac{75}{2}.

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Bas_tet [7]
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7 0
2 years ago
To add 20.4 + 3.75 + 4.25, Crystal first added 3.75 and 4.25. Which property did Crystal use to add mentally?
evablogger [386]

Answer:

Associative Property of Addition

Step-by-step explanation:

From the list of given options, option A correctly answers the question and this is because

a + b + c = a + (b + c) --- (1)

or

a + b + c = (a + b) + c --- (2)

<em>The above illustrations only apply to Associative Property of Addition</em>

In Crystal's case:

20.4 + 3.75 + 4.25 = 20.4 + (3.75 + 4.25)

This can be compared to (1) above

Hence;

<em>Option A answers the question</em>

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