If LM = 3x + 5, MN = 4x, and LN

Mathematics

1 answer:

tia_tia [17]2 years ago

5 0

We have that x = 3, LM = 14 and LN = 2. options A, C and E

<h3>How to determine the value</h3>

We known that the three sides are on a straight line

LM + MN = LN

Let's substitute the values, we have

3x + 5 + 4x = 11x - 7

Collect like terms

3x + 4x - 11x = -7 -5

-4x = -12

x = -12/ -4

x = 3

LM = 3x + 5 = 3(3) + 5 = 14

LN = 11x - 7 = 11(3) -7 = 33 -7 = 26

Thus, we have that x = 3, LM = 14 and LN = 2. options A, C and E

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S is the centroid of triangle NQL. What is the length of NR?

svetoff [14.1K]

ANSWER

The length of NR is
$36 \: \: units$

EXPLANATION

The centroids divides the medians in the ratio
$2:1$
For instance

$|NS|:|SR|=2:1$

But

$|NS| = 9n - 12$

$|SR|=3n$

We substitute all these values in to the above relation to obtain,

$(9n - 12):3n=2:1$

This can be rewritten as

$\frac{9n - 12}{3n} = \frac{2}{1}$

We cross multiply to obtain,

$1(9n - 12) = 2 \times 3n$

This implies that,

$9n - 12 = 6n$

We group like terms to obtain,

$9n - 6n = 12$

This simplifies to give us,

$3n = 12$

$n = 4$

We can now determine each length as follows,

$|NS| = 9(4 ) - 12$

$|NS| = 36- 12$

$|NS| = 24$

$|SR|=3 \times 4$

$|SR|=12$

From the diagram,

$|NR|=|NS|+|SR|$

$|NR|=24 + 12$

$|NR|=36 \: units$