Mathematics: Given: △abc, ab=bc=10 cm, ac=12 cm, ak ⊥ bc cm ⊥ ab , bn ⊥ ac . find: ak, bn, cm.

Given: △abc, ab=bc=10 cm, ac=12 cm, ak ⊥ bc cm ⊥

Ответ:

elisakgarcia2007

11.03.2022

Since AB=Bc, triangle ABC is isosceles with base AC. Then BN is height and median drawn to the base. If BN is median and AC=12 cm, then AN=NC=6 cm.

1. By the Pythagorean theorem for triangle ABN,

$AB^2=AN^2+BN^2,\\ \\10^2=6^2+BN^2,\\ \\BN^2=100-36=64,\\ \\BN=8\ cm.$

2. AB and BC are legs of isosceles triangle ABC. The heights drawn to the lags of isosceles triangle are congruent, so AK=CM. Consider two right triangles AKC and AKB. By the Pythagorean theorem,

$AC^2=AK^2+KC^2,\\ \\AB^2=BK^2+AK^2=(BC-KC)^2+AK^2.$

Subtract from the second equation the first one:

$AB^2-AC^2=(BK-KC)^2-KC^2,\\ \\10^2-12^2=(10-KC)^2-KC^2,\\ \\100-144=100-20KC+KC^2-KC^2,\\ \\-144=-20KC,\\ \\KC=7,2\ cm.$

Then

$AK^2=AC^2-KC^2,\\ \\AK^2=12^2-7.2^2=144-51,84=92.16,\\ \\AK=9.6\ cm.$

AK=CM=9.6 cm, BN=8 cm

0,0(0 оценок)

Ответ:

hailie2002

12.11.2020

Mathematics

The median is 38.5

The lower quartile is 29

There is an outlier (154)

The upper quartile is 70

and

The interquartile range is 70 - 29= 41

Hope this helps u!

0,0(0 оценок)

Given: △abc, ab=bc=10 cm, ac=12 cm, ak ⊥ bc cm ⊥ ab , bn ⊥ ac . find: ak, bn, cm.

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question