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# What is the area of the triangle shown above?

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Math Expert
Joined: 02 Sep 2009
Posts: 65194
What is the area of the triangle shown above?  [#permalink]

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23 Aug 2018, 02:41
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5% (low)

Question Stats:

90% (00:59) correct 10% (00:54) wrong based on 40 sessions

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What is the area of the triangle shown above?

A. $$\frac{25\sqrt{2}}{3}$$

B. $$\frac{25\sqrt{3}}{2}$$

C. 25

D. $$25\sqrt{2}$$

E. $$25\sqrt{3}$$

Attachment:

image007.jpg [ 2.53 KiB | Viewed 778 times ]

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What is the area of the triangle shown above?  [#permalink]

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23 Aug 2018, 02:50
Bunuel wrote:

What is the area of the triangle shown above?

A. $$\frac{25\sqrt{2}}{3}$$

B. $$\frac{25\sqrt{3}}{2}$$

C. 25

D. $$25\sqrt{2}$$

E. $$25\sqrt{3}$$

Attachment:
image007.jpg

The given triangle is a 30-60-90 triangle.

So, the sides are in the ratio $$x:\sqrt{3}x:2x$$
Given, 2x=10 or, x=5

So, base=x=5, $$height=\sqrt{3}x=5\sqrt{3}$$
So, $$Area=1/2*base*height=1/2*5*5\sqrt{3}=\frac{25\sqrt{3}}{2}$$

Ans. (B)
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What is the area of the triangle shown above?  [#permalink]

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29 Mar 2020, 06:15
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Top Contributor
Bunuel wrote:

What is the area of the triangle shown above?

A. $$\frac{25\sqrt{2}}{3}$$

B. $$\frac{25\sqrt{3}}{2}$$

C. 25

D. $$25\sqrt{2}$$

E. $$25\sqrt{3}$$

Attachment:
image007.jpg

Since angles in a triangle must add to 180°, we can see that the missing angle is 60°, which means we have a Special 30-60-90 Special Triangle
So let's compare the given 30-60-90 triangle with the base 30-60-90 triangle

In the base triangle, the side opposite the 90-degree angle has length 2, and in the given triangle, the side opposite the 90-degree angle has length 10
10/2 = 5, which means the given triangle is 5 times the size of the base triangle

Now that we know the Magnification Factor, we can determine the lengths of the remaining sides.

In the base 30-60-90 triangle, the side opposite the 30-degree angle has length 1
So, in the given triangle, x = (5)(1) = 5

Likewise, in the base 30-60-90 triangle, the side opposite the 60-degree angle has length √3
So, in the given triangle, x = (5)(√3) = 5√3
We get:

We now have enough information to find the area of a triangle.

Area of triangle = (base)(height)/2
If we let side AC be the base, and let side CB be the height, then the area = (5)(5√3)/2 = (25√3)/2

Cheers,
Brent
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What is the area of the triangle shown above?   [#permalink] 29 Mar 2020, 06:15