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# 1) Two similar triangles with the 3 angles of each triangle

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Intern
Joined: 29 Oct 2006
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1) Two similar triangles with the 3 angles of each triangle [#permalink]  12 Nov 2006, 01:33
1) Two similar triangles with the 3 angles of each triangle measuring x, y and z each. If the area of 1 of the triangles is twice the area of the other triangle, then the base of the larger triangle is how many times the base of the smaller triangle?
a. sq rt (2) / 2
b. sq rt (3) / 2
c. sq rt (2)
d. sq rt (3)
e. 2
OA after a few posts...
SVP
Joined: 01 May 2006
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(C) for me

Let define:
> B and H, the base and the height of the bigger triangle
> b and h, the base and the height of the smaller triangle

As the triangles are similar, it exists a factor k such that:
o B=k*b
o H=k*h

We know as well that:
o Area Bigger Triangle = 2*Area smaller Triangle

Thus,
B*H/2=b*h
<=> (k*b)*(k*h)=2*b*h
<=> k^2=2
=> k = sqrt(2) as a lenght is always positive.
Intern
Joined: 29 Oct 2006
Posts: 15
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Fig wrote:
(C) for me

Let define:
> B and H, the base and the height of the bigger triangle
> b and h, the base and the height of the smaller triangle

As the triangles are similar, it exists a factor k such that:
o B=k*b
o H=k*h

We know as well that:
o Area Bigger Triangle = 2*Area smaller Triangle

Thus,
B*H/2=b*h
<=> (k*b)*(k*h)=2*b*h
<=> k^2=2
=> k = sqrt(2) as a lenght is always positive.

thanks mate....great explanation....
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