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# If the area of the triangle in the figure above is 100, what is the le

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If the area of the triangle in the figure above is 100, what is the le [#permalink]

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19 Aug 2017, 10:06
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Difficulty:

15% (low)

Question Stats:

88% (00:31) correct 12% (01:15) wrong based on 68 sessions

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If the area of the triangle in the figure above is 100, what is the length of side AB?

(A) 10√3
(B) 10√5
(C) 20
(D) 24
(E) 25

Attachment:

2017-08-19_2104.png [ 11.52 KiB | Viewed 1899 times ]

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If the area of the triangle in the figure above is 100, what is the le [#permalink]

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19 Aug 2017, 10:14

Since we have BC = 20 and we know that the triangle ABC is right angled at B,

We are also given area of the triangle = 100
Area = $$\frac{1}{2} * Base * Height = 100$$
BC is the Height and let x be the Base(AC)

$$\frac{1}{2}*x*20 = 100$$
$$x = \frac{200}{20}$$ => $$x = 10$$

In a right angled triangle, using Pythagoras theorem
$$AB^2 = AC^2 + BC^2$$
$$AB^2 = 400 + 100 = 500$$
$$AB = \sqrt{500} = \sqrt{5*10*10}$$
Therefore the length of AB = $$10\sqrt{5}$$ (Option B)
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Re: If the area of the triangle in the figure above is 100, what is the le [#permalink]

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19 Aug 2017, 10:18
Ans is B

0.5 AC x BC = 100 , where AC =20
BC= 10

using pythogoras theorm AC^2+BC^2 =AB^2
AB= √500
= 10√5

hence B is correct
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Re: If the area of the triangle in the figure above is 100, what is the le [#permalink]

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19 Aug 2017, 10:20
Bunuel wrote:

If the area of the triangle in the figure above is 100, what is the length of side AB?

(A) 10√3
(B) 10√5
(C) 20
(D) 24
(E) 25

Attachment:
2017-08-19_2104.png

Area of triangle ABC = $$\frac{1}{2}*BC*AC = 100$$
or,$$\frac{1}{2}*20*AC = 100$$. therefore $$AC = 10$$
$$AB$$ = $$\sqrt{AC^2 + BC^2}$$

Therefore $$AB$$ = $$\sqrt{20^2 + 10^2}$$ $$= 10\sqrt{5}$$

Option B
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Re: If the area of the triangle in the figure above is 100, what is the le [#permalink]

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19 Aug 2017, 10:20
Bunuel wrote:

If the area of the triangle in the figure above is 100, what is the length of side AB?

(A) 10√3
(B) 10√5
(C) 20
(D) 24
(E) 25

Attachment:
2017-08-19_2104.png

100=(1/2)*20*x
x=10

AB is the hypotenuse, therefore
20^2+10^2=(AB)^2
AB^2=500
AB=10√5

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If the area of the triangle in the figure above is 100, what is the le [#permalink]

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19 Aug 2017, 20:48
Bunuel wrote:

If the area of the triangle in the figure above is 100, what is the length of side AB?

(A) 10√3
(B) 10√5
(C) 20
(D) 24
(E) 25

Attachment:
2017-08-19_2104.png

1. Area = $$\frac{1}{2}$$ * base * height.
2. Area = 100 = $$\frac{1}{2}$$ * AC * BC. Plug the info, we find AC = 10.
3. Find AB using Pythagoras : AB^2 = AC^2 * BC^2. AB^2 = 500, thus AB = $$10\sqrt{5}$$.

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If the area of the triangle in the figure above is 100, what is the le   [#permalink] 19 Aug 2017, 20:48
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