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# In the figure, angle C and angle M are right angles, and KL = 10. If

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Joined: 22 Dec 2015
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In the figure, angle C and angle M are right angles, and KL = 10. If  [#permalink]

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28 Dec 2015, 13:54
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60% (01:20) correct 40% (01:15) wrong based on 179 sessions

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In the figure, angle C and angle M are right angles, and KL = 10. If the area of triangle ABC is four times the area of triangle KLM, what is the length AB?

(1) Angles ABC and KLM have the same measure.

(2) LM is 6 inches.

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Joined: 02 Aug 2009
Posts: 6551
Re: In the figure, angle C and angle M are right angles, and KL = 10. If  [#permalink]

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28 Dec 2015, 19:44
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dflorez wrote:
In the figure, angle C and angle M are right angles, and KL = 10. If the area of triangle ABC is four times the area of triangle KLM, what is the length AB?

(1) Angles ABC and KLM have the same measure.

(2) LM is 6 inches.

Hi,
you are given two right angle triangle and a side of one triangle is given..
Also given is the ratio of ares of two triangles..
we are asked for length of a side of first triangle..

lets see the statement..
(1) Angles ABC and KLM have the same measure.
we are given another angle to be equal ..
now we have two triangles with all three angles same, which means that the two triangles are similar..
In similar triangles, the ratio of area is square of the ratio of corresponding sides ..
it is given four times, so the ratio of sides is two times..
since KL is 10, AB will be 2* 10=20..
suff

(2) LM is 6 inches...
with this info we know what is the area of triangle KLM, and thus the area of ABC, but there will be various combinations of sides to get that area..
insuff..

ans A
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Re: In the figure, angle C and angle M are right angles, and KL = 10. If  [#permalink]

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29 Dec 2015, 01:40
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1
dflorez wrote:
In the figure, angle C and angle M are right angles, and KL = 10. If the area of triangle ABC is four times the area of triangle KLM, what is the length AB?

(1) Angles ABC and KLM have the same measure.

(2) LM is 6 inches.

Similar question to practice: the-area-of-the-right-triangle-abc-is-4-times-greater-than-127070.html
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Re: In the figure, angle C and angle M are right angles, and KL = 10. If  [#permalink]

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29 Dec 2015, 15:42
1
Given the area of $$\triangle ABC$$ = 4 x Area of $$\triangle KLM$$.
Both these triangles are right angled at C and M respectively.

KL = 10

To find: Length of AB.

Statement 1.

This tells us that the triangles are similar. Hence the ratios of the sides are equal.

Area of $$\triangle ABC$$ = 4 x Area of $$\triangle KLM$$or 1/2 x AC x CB = 4 x 1/2 x KM x LM; i.e. $$4 = \frac{(AC X CB)}{(KM X LM)}$$ - Lets call this equation 1.
As the triangles are similar $$\frac{AC}{KM} =\frac{CB}{LM} = \frac{AB}{KL}$$

So equation 1 reduces to $$(\frac{AB}{KL})^2 = 4$$. Since we know the value of KL (=10) we can find the value of AB.

Hence statement 1 is sufficient.

Or simply use the formula ratios of the areas of similar triangles = square of the ratios of corresponding sides. Above is just a derivation of the formula.

Statement 2 .

Information in statement 2 helps us calculate the third side of triangle KLM but little else.
No relationship between sides of the 2 triangles has been mentioned.

Statement 2: Insufficient on its own.

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Re: In the figure, angle C and angle M are right angles, and KL = 10. If  [#permalink]

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13 Mar 2017, 05:21
STE 1: With the given information we can prove that both the triangles are similar. If two similar triangles have corresponding lengths in ratio a:b then their area will be in ratio a^2:b^2 and their volume will be in ratio a^3:b^3.sufficient

STE 2 : No information. Not sufficient
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Re: In the figure, angle C and angle M are right angles, and KL = 10. If  [#permalink]

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01 Aug 2018, 03:52
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Re: In the figure, angle C and angle M are right angles, and KL = 10. If &nbs [#permalink] 01 Aug 2018, 03:52
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