IF THE TRIANGLES IN THE ABOVE FIGURE ARE PROPORTIONAL, WHATS THE LENGTH OF SIDE B?

Mathematics

1 answer:

Tema [17]3 years ago

5 0

<h3>Answer: choice B) 36</h3>

=================================================

Explanation:

The vertical sides, when read from left to right, can be divided to get this fraction: 9/90

Following the same order and direction, we divide the slanting corresponding sides to get: b/360

The fractions we constructed are equal to one another, as the triangles are said to be proportional.

We have the fraction 9/90 = b/360

Lets cross multiply and solve for b

--------------------

9/90 = b/360

9*360 = 90*b

3240 = 90b

90b = 3240

90b/90 = 3240/90

--------------------

A quick way to do this may be to notice how the jump from 9 to 90 is "times 10" so the jump from b to 360 is also "times 10". Think in reverse to divide 360 over 10 and we land on 36 as our answer. This line of thinking does not work as simple for all proportional problems.

You might be interested in

Which exponential equation is equivalent to the logarithmic equation below? c = ln 2

Sophie [7]

$\text{A logarithmic lemma: } \\ \text{It follows that: } \log_a a = 1$
$\text{Following this property, we can see that: } a^{\log_{a} a} = a$
$\text{Furthermore, we can create more general properties: } a^{\log_a b} = b$

$c = \log_e 2 \Rightarrow e^{c} = e^{\log_e 2} \\ \text{Using our third property, we see that: } e^{c} = 2$
$\text{And finally, this works for any } \log_{a} b \left\{a > 0, b \in \mathbb{R}\right\}$