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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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New post 19 Aug 2017, 10:06
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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


[Reveal] Spoiler:
Attachment:
2017-08-19_2104.png
2017-08-19_2104.png [ 11.52 KiB | Viewed 1666 times ]
[Reveal] Spoiler: OA

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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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New post 19 Aug 2017, 10:14
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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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New post 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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New post 19 Aug 2017, 10:20
Bunuel wrote:
Image
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


[Reveal] Spoiler:
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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New post 19 Aug 2017, 10:20
Bunuel wrote:
Image
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


[Reveal] Spoiler:
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

Answer: B

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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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New post 19 Aug 2017, 20:48
Bunuel wrote:
Image
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


[Reveal] Spoiler:
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 = \(10\sqrt{5}\).

Answer is B.
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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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