Основания BC и AD трапеции ABCD равны 3 и 6, диагонали пересекаются в точке О, с...

July 2022 1 10 Report

Основания BC и AD трапеции ABCD равны 3 и 6, диагонали пересекаются в точке О, сумма площадей треугольников АОВ и СОD равна 40. Найдите высоту трапеции.

Answers & Comments

Матов

Verified answer

Если в сумме $S_{AOB}+S_{COD}=40\\
S_{AOB}=S_{COD}\\
S_{AOB}=20\\\\
S_{ABCD}=\frac{9}{2}*h\\
$ треугольники $BOC \ \ \ AOD$ подобны , если из подобия
$\frac{3}{6}=\frac{x}{h-x}\\
4.5h-40=\frac{3x}{2}+\frac{6(h-x)}{2}\\
9h-80=6h-3x\\
3h-80=-3x\\
3h+3x=80\\
h+x=\frac{80}{3}\\
\frac{3}{6}=\frac{\frac{80}{3}-h}{h-\frac{80}{3}+h} \\
2h-\frac{80}{3}=\frac{160}{3}-2h\\
4h=80\\
h=20$
Ответ 20

2 votes Thanks 6

Answers & Comments

Verified answer

How many mistakes in spelling are there in a sentence? She thinks hihgly of Aga...

Choose the right variant to complete the sentence. Walk!... A) No run! B) Not ...

choose the right sentence a has she told you the good news yet b good morn

choose the words with the same meaning not weeds a flowers b vegetables v

Choose the sentence which is incorrect. A) I don't like reading but my friend is...

privedite sobstvennyj primer kakoj libo deyatelnosti i raskrojte na etom primere19815314c5640e1d40c63c136bbf772e 54885

perevedite predlozhenie on spit 10 chasov pora ego budit

ukazhite v kakih predlozheniyah nuzhna zapyataya pered soyuzom i obyasnite pochemu1 p

najdite vysotu trapecii esli ee diagonali vzaimno perpendikulyarny i ravny 15 i

diagonali trapecii abcd peresekayutsya v tochke o osnovaniya bc i ad ravny 3 i 4 a4c3093b5d2eb86c2c8c1d934db1d6772 66950

рекомендуемые вопросы

Helpful Links

Helpful Social