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Gaurav Seth 4 years, 8 months ago
In an equilateral ABC, D is a point on side BC such that Prove that 9AD2 = 7AB2.
Given : An equilateral triangle ABC such that To Prove : 9AD2 = 7AB2
Const: Draw AE ⊥ BC.
Proof: In right triangles ABE and ACE, we have
AE = AE [common]
∠AEB = ∠AEC [90°]
and AB = AC
[∆ABC is an equilateral]
Therefore, by using RHS congruent condition
BE = CE [by CPCT]
In right triangle ADE, we have
But AB = BC = CA
Posted by Manshi Raj 4 years, 8 months ago
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Posted by Laxmi Narayan 4 years, 8 months ago
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Yogita Ingle 4 years, 8 months ago
Ap=BP ....(length of tangents from external point to circle are equal)
∠A=∠B=90o .... (Tangent is ⊥ to radius)
OP=OP .... (common side)
∴△AOP≅△BOP ....(RHS test of congruence)
∠APO=∠BPO=30o→c.a.c.t
∠AOP=∠BOP=60o→c.a.c.t
△AOP is 30o−60o−90o triangle.
∴△AOP,
cos60=OPOA
OP= a/ 1/2=2a
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Kunwar Dev Singh 4 years, 8 months ago
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Yogita Ingle 4 years, 8 months ago
given, x2−6x+5=0
x2−5x−x+5=0
x(x−5)−1(x−5)=0
(x−5)(x−1)=0
x=5,1
Posted by Sumit Rathi 4 years, 8 months ago
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Yogita Ingle 4 years, 8 months ago
Let us assume thenumerator to be =x
Let us assume thedenominator to be =y
Hence the fractionbecomes=x/y
Accordingtothe given condition
(x−1)/y=1/3
⇒y=3x−3 ———-(i)
Accordingtothesecond givencondition,
x/(y+8)=1/4
⇒y+8=4x
⇒y=4x−8 ————(ii)
Combining(i)and(ii) we get,
3x−3=4x−8
⇒3x−4x=−8+3
−x=−5
⇒x=5
from(i)
y=15−3=12
So,the fraction is =5/12
Posted by Ranvijay Kumar 4 years, 8 months ago
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Malaika Sharma 4 years, 8 months ago
Posted by Charvi Sangwan 4 years, 3 months ago
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Sia ? 4 years, 3 months ago
The time taken by one man alone is 140 days and the time taken by one boy alone is 280 days .
Step-by-step explanation:
Let time taken by one man alone be = x days
Let time taken by one boy alone be = y days
According to question
.......(1)
and .......(2)
Solve equation (1) and (2) by eliminating,
Multiply equation (1) by 2 and equation (2) by 3 then subtract
...... (3)
.......(4)
Subtract equation (4) from equation (3)
so, the time taken by one man alone is 140 days
Put value of x in equation (1)
Subtract both the sides by
Multiply both the sides by
Multiply both the sides by 280,
so, the time taken by one boy alone is 280 days
Therefore, the time taken by one man alone is 140 days and the time taken by one boy alone is 280 days .
Posted by Charvi Sangwan 4 years, 8 months ago
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Yogita Ingle 4 years, 8 months ago
Let one number be X. The other number be Y.
GIVEN,
x+y=8
x=8-y ---------------(1)
1/x+1/y=8/15
BY SIMPLIFING 1/x+1/y=8/15 WE GET,
(x+y)/xy=8/15
FROM (1) WE GET,
8/8y-y2=8/15
y2-8y+15=0
(y - 3)(y - 5) = 0
y = 3 or 5
WE KNOW THAT x+y=8
When y=5, x=3
When y = 3, x = 5
Posted by Eucharist Lover 4 years, 8 months ago
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Yogita Ingle 4 years, 8 months ago
Simple Interest = P × R × T ÷ 100
So S.I in first yr. ⇒ P x R x T / 100
⇒ 1000 x 1 x 8 ÷ 100
⇒ 80
In second Yr. ⇒ 1000 x 2 x 8 ÷ 100
⇒ 160
Similarly in third Yr. ⇒ 240
So , we get the A.P. like this i.e. 80, 160, 240
Therefor a= 80 , d= 80.
we have to find out the interest at the end of 30 yr.
⇒ a = a + ( n-1 ) d
⇒ 80 + ( 30 - 1 ) 80
⇒ 80 + 29 × 80
⇒ 2400
There fore , the Interest at the end of 30 yrs is 2400
Posted by Ayush Kumar 4 years, 8 months ago
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Secret ??? 4 years, 8 months ago
Secret ??? 4 years, 8 months ago
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Rajat Arora 4 years, 8 months ago
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