To find: The values of KP, KM, MR, ML, MN and PR.Given:12210203131.jpgbar(PR)||bar(KL) = 9, ln = 16, PM = 2(KP)KM=KP+PM=3KP

Chaya Galloway 2021-01-10 Answered

To find: The values of KP, KM, MR, ML, MN and PR.
Given:
image
\(\displaystyle\overline{{{P}{R}}}{\mid}{\mid}\overline{{{K}{L}}}={9},{\ln{=}}{16},{P}{M}={2}{\left({K}{P}\right)}\)
KM=KP+PM=3KP

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

funblogC
Answered 2021-01-11 Author has 14694 answers

Conclusion:
By A-A similarity, it can be proved that:
\(\displaystyle\triangle{L}{M}{K}\sim\triangle{M}{N}{K}\)
Similar triangles have corresponding sides as proportional.
\(\displaystyle\frac{{{M}{K}}}{{{L}{K}}}=\frac{{{N}{K}}}{{{M}{K}}}\)
\(\displaystyle\Rightarrow\frac{{{3}{K}{P}}}{{25}}=\frac{{9}}{{{3}{K}{P}}}\)
\(\displaystyle\Rightarrow{K}{P}={5}\)
\(\displaystyle\Rightarrow{K}{M}={3}{K}{P}={15}\)
By A-A similarity, it can be proved that:
\(\displaystyle\triangle{L}{M}{K}\sim\triangle{R}{M}{P}\)
Similar triangles have corresponding sides as proportional.
\(\displaystyle\frac{{{M}{K}}}{{{L}{K}}}=\frac{{{P}{M}}}{{{R}{P}}}\)
\(\displaystyle\Rightarrow\frac{{15}}{{25}}=\frac{{10}}{{{R}{P}}}\)
\(\displaystyle\Rightarrow{K}{P}={16}\frac{{2}}{{3}}\)
Using Pythagorean Theorem in right angled triangle \(\displaystyle\triangle{L}{M}{K}\):
\(\displaystyle{H}{y}{p}{o}{t}{e}nu{s}{e}^{{2}}={B}{a}{s}{e}^{{2}}+{P}{e}{r}{p}{e}{n}{d}{i}{c}ul{{a}}{r}^{{2}}\)
\(\displaystyle={25}^{{2}}={15}^{{2}}+{L}{M}^{{2}}\)
\(\displaystyle\Rightarrow{L}{M}^{{2}}={400}\)
\(\displaystyle\Rightarrow{L}{M}={20}\)
In similar triangles: \(\displaystyle\triangle{L}{M}{K}\sim\triangle{M}{N}{K}\)
Ratio can be written as:
\(\displaystyle\frac{{{L}{M}}}{{{M}{K}}}=\frac{{{M}{N}}}{{{N}{K}}}\)
\(\displaystyle\Rightarrow\frac{{20}}{{15}}=\frac{{{M}{N}}}{{9}}\)
\(\displaystyle\Rightarrow{M}{N}={12}\)
\(\displaystyle{K}{P}={5},{K}{M}={15},{M}{R}={13}\frac{{1}}{{3}},{M}{L}={20},{M}{N}={12},{P}{R}={16}\frac{{2}}{{3}}\)

Not exactly what you’re looking for?
Ask My Question
42
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2020-11-05

Triangle MPT with \(\displaystyle\overline{{{N}{R}}}{\mid}{\mid}\overline{{{M}{T}}}\) is shown below. The dimensions are in centimeters.
image
Which measurement is closest to the length of \(\displaystyle\overline{{{R}{T}}}\) in centimeters?
1)1.4
2)1.8
3)3.4
4)4.3

asked 2021-11-03
Given:
\(\displaystyle\triangle{M}{\ln},\overline{{{M}{L}}}={13},\overline{{{M}{N}}}={6},\overline{{{N}{L}}}={10},\triangle{R}{Q}{S},\overline{{{R}{Q}}}={39},\overline{{{R}{S}}}={18},\overline{{{S}{Q}}}={30}\)
Find the scale factor from \(\displaystyle\triangle{M}{\ln{}}\) to \(\displaystyle\triangle{R}{Q}{S}\).
asked 2021-08-17

Given:
\(\displaystyle\triangle{M}LN,\overline{{{M}{L}}}={13},\overline{{{M}{N}}}={6},\overline{{{N}{L}}}={10},\triangle{R}{Q}{S},\overline{{{R}{Q}}}={39},\overline{{{R}{S}}}={18},\overline{{{S}{Q}}}={30}\)
Find the scale factor from \(\displaystyle\triangle{M}LN\) to \(\displaystyle\triangle{R}{Q}{S}\).

asked 2021-02-21

State the third congruence required to prove the congruence of triangles using the indicated postulate.
image
a)\(\displaystyle\overline{{{Z}{Y}}}\stackrel{\sim}{=}\overline{{{J}{L}}}\)
b)\(\displaystyle\angle{X}\stackrel{\sim}{=}\angle{K}\)
c)\(\displaystyle\overline{{{K}{L}}}\stackrel{\sim}{=}\overline{{{X}{Z}}}\)
d)\(\displaystyle\angle{Y}\stackrel{\sim}{=}\angle{L}\)

asked 2021-05-16

To prove : The similarity of \(\displaystyle\triangle{N}{R}{T}\) with respect to \(\displaystyle\triangle{N}{S}{P}\).
Given information: Here, we have given that \(\displaystyle\overline{{{S}{P}}}\) is altitude to \(\displaystyle\overline{{{N}{R}}}\ {\quad\text{and}\quad}\ \overline{{{R}{T}}}\) is altitude to \(\displaystyle\overline{{{N}{S}}}\).

asked 2020-11-01

To calculate:The ratio of line AB and BC.
Given information:
The following diagram is given
image

asked 2020-10-27

To check: whether the triangles are similar. If so, write a similarity statement.
Given:
The given triangles are:
image

...