All categories

3 years ago

P is the centroid of △JLN, LO⊥JN, ∠NJK≅∠JNM, OP=8, OJ=15. Find the perimeter of △JLN.

Mathematics

1 answer:

umka2103 [35]3 years ago

8 0

The complete question in the attached figure

we know that
The Centroid of a Triangle is the point where the three medians of the triangle intersect.
Each median divides the triangle into two smaller triangles of equal area.
and
the centroid divides each median into two segments whose lengths are in the ratio 2:1, with the longest one nearest the vertex

therefore

triangles LOJ and LON are similar
ON=OJ=15 units
then
NJ=15+15-------> NJ=30 units

Let
x--------> distance OL
so
OP=x/3
OP=8
x/3=8--------> x=8*3---------> x=24 units
OL=24 units

in the right triangle JLO
OJ=15 units
OL=24 units
JL=?
applying the Pythagorean Theorem
JL²=OJ²+OL²--------> JL²=15²+24²------> JL=28.30 units

perimeter of triangle JLN
P=JL*2+NJ-------> P=2*28.30+30------> P=86.60 units------> P=86.6 units

the answer is
the perimeter of △JLN is 86.6 units

You might be interested in

Two sides of a triangle have measures 3 ft and 6 ft. Also, these sides form a vertex whose angle measures 60 degrees. Calculate

Basile [38]

Answer:

A. The length of the third side is approximately 5 feet.

B. A = $88^{o}$ , B = $60^{o}$ and C = $32^{o}$ .

Step-by-step explanation:

Let the triangle be ABC. Given two sides and an included angle, let us apply the cosine rule to determine the third length.

A. Let side a = 6 feet and c = 3 feet, thus;

$b^{2}$ = $a^{2}$ + $c^{2}$ - 2ac Cos B

= $6^{2}$ + $3^{2}$ - 2(6 x 3) Cos $60^{o}$

= 36 + 9 - 36 x 0.5

= 45 - 18

$b^{2}$ = 27

b = $\sqrt{27}$

= 5.1962

b = 5.2 feet

b ≅ 5 feet

The length of the third side is approximately 5 feet.

B. Given that B = $60^{o}$ , then let us apply the Sine rule to determined the measure of A.

$\frac{a}{SinA}$ = $\frac{b}{SinB}$

So that,

$\frac{6}{Sin A}$ = $\frac{5.2}{Sin60^{o} }$

Sin A = $\frac{0.886*6}{5.2}$

Sin A = 0.99923

A = $Sin^{-1}$ 0.99923

= 87.75

A ≅ $88^{o}$

Since the sum of angle in a triangle = $180^{o}$ .

Then,

A + B + C = $180^{o}$

$88^{o}$ + $60^{o}$ + C = $180^{o}$

$148^{o}$ + C = $180^{o}$

C = $180^{o}$ - $148^{o}$

= $32^{o}$

C = $32^{o}$

Thus,

A = $88^{o}$ , B = $60^{o}$ and C = $32^{o}$ .

5 0

3 years ago

It is estimated that 7 out of 10 people invited to a wedding will attend. If Mark and Katie invite 120 people, how many should t

Margarita [4]

7 and 10 is half

so we expect the people come to wedding half of 120÷2=60 people

i just try

5 0

3 years ago

3) When Jackie took her children to the movie theater, she bought one box of candy and three small drinks for

Nezavi [6.7K]

Answer:

c + 3d = 14.75

2c + 5d = 26

A box of candy is $4.25 and a drink is $3.50

Step-by-step explanation:

Let c represent the cost of a box of candy and let d represent the cost of a drink

c + 3d = 14.75

2c + 5d = 26

Solve by elimination by multiplying the top equation by -2

-2c - 6d = -29.5

2c + 5d = 26

Add them together

-d = -3.5

d = 3.5

Plug in 3.5 as d into one of the equations to solve for c

c + 3d = 14.75

c + 3(3.5) = 14.75

c + 10.5 = 14.75

c = 4.25

So, a box of candy is $4.25 and a drink is $3.50

6 0

2 years ago

11,11,11,12,12,13,14,14,15 find the median

makvit [3.9K]

the median out of the data set is.

12.

to find the median, you have to,

The median is also the number that is halfway into the set. To find the median, the data should be arranged in order from least to greatest. If there is an even number of items in the data set, then the median is found by taking the mean (average) of the two middle-most numbers.

6 0

3 years ago

CB = 4, CA = 11 , and CE = 8 , what is the length of overline ET ?

erma4kov [3.2K]