ΔABD and ΔACD are similar (By A-A-A) and The length of DA is 6.
The triangles where all the corresponding sides of the two triangles are in equal proportion are called similar triangles.
In triangle ΔABC ∠BAC=90°
Let ∠ABC=x
then ∠ACB=90°-x
In triangle ΔADC, ∠ADC =90°
∠ACB=∠ACD=90°-x
∠DAC= 180°-(∠ADC+∠ACD)= 180°-(90°+90°-x)= x
In triangle ΔADB , ∠ADB =90°
∠ABD=x
∠BAD=90°-x
Between triangles ΔABD and ΔACD
∠ABD=∠DAC (=X)
∠BAD∠ACD (=90°-x)
∠ADB=∠ADC (=90°)
from the above, it is clear that triangles ΔABD nad ΔACD is similar. (By A-A-A)
So sides are in equal proportion in 2 triangles,
AD/DC= BD/AD
⇒AD²= BD*DC
⇒AD²=9*4
⇒AD²=36
⇒AD=6
⇒DA=6
Therefore triangles ΔABD and ΔACD are similar (By A-A-A) and The length of DA is 6.
Learn more about similar triangle
here: brainly.com/question/14285697
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Answer:
a^2b(7 + 10b + 14b^2)
Step-by-step explanation:
Each term contains a factor of a^2b. Factoring that out gives the answer above.
Answer:
200 berlindes
Step-by-step explanation:
Vamos representar
O número total de berlindes na caixa = X
Mármores vermelhos = 20% de X
= 0.2X
Mármores amarelos = 40% de X
= 0.4X
Mármores azuis = 80
Conseqüentemente,
0.2X + 0.4X + 80 = X
Recolher termos semelhantes
80 = X - 0.2X - 0.4X
80 = X - 0.6X
80 = 0.4X
Divida ambos os lados por 0.4
X = 80 / 0.4
X = 200
Uma vez que X representa o número total de berlindes na caixa, portanto, o número total de berlindes na caixa = 200 berlindes
2(4x-1) + 3x = 8x - 2 + 3x
= 11x - 2
Hope this helps
The question requires getting the length of TV
<u><em>Answer:</em></u>TV = 36.2 in
<u><em>Explanation:</em></u>We are given that point T lies on line QV. The scenario is shown in the attached image.
<u>This means that:</u>
QV = QT + TV
<u>We have:</u>
QT = 28.5 in
QV = 64.7 in
<u>Substitute with the values to get the length of TV as follows:</u>
QV = QT + TV
64.7 = 28.5 + TV
TV = 64.7 - 28.5
TV = 36.2 in
Hope this helps :)
