In the figure, ABCD is a rectangle, and the area of triangle ACE is 10

Question

https://gmatclub.com/forum/download/file.php?id=39178 In the figure, ABCD is a rectangle, and the area of triangle ACE is 10, what is the area of rectangle ? A. 18 B. 22.5 C. 36 D. 54 E. 60 Untitled.png

Bunuel · Answer

area_{ACE}=\frac{1}{2}*base*height=\frac{1}{2}*CE*AB=10 ;

\frac{1}{2}*5*AB=10 ;

AB=4 .

area_{ABCD}=AB*CB=AB*(CE+EB)=4*9=36 .

Answer: C.

hirendhanak · Answer

thanks bunuel

I was not clear why we took AB as the height of triangle ACE . because AB is out of scope of the triangle ACE.

I thought AE becomes height of the triangle ACE.

Bunuel · Answer

The height of a triangle is the perpendicular from the base to the opposite vertex,  sometimes the base may need to be extended . Since there are three possible bases, there are also three possible heights, so if we consider the base to be CE then the height will be the perpendicular from CE (CB) to the opposite vertex A, thus height is AB.

TheUltimateWinner · Answer

In the figure, ABCD is a rectangle, and the area of triangle ACE is 10. What is the area of the rectangle? 24.PNG A. 18 B. 22.5 C. 36 D. 44 E. 45

chetan2u · Answer

Area of a triangle is height*base/2...
In ∆ACE, CE is the base and height is CD...
So CE*CD/2 = 10.....5*CD=20.....CD is 4...

So the two sides of the rectangle ABCD are 4 and (5+4) or 9..
Thus Area of rectangle is 4*9=36
C

TheUltimateWinner · Answer

Thank you  chetan2u

pushpitkc · Answer

I have a small doubt regarding this question, how can we consider CD an altitude for the triangle ACE?

TheUltimateWinner · Answer

That was also my question but end of the day we have to take it as altitude !

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abhimahna · Answer

Height of a triangle is defined as the perpendicular distance from one of the vertices to its base.

So, If we are considering CE a base of the triangle. The perpendicular distance from C to its base is CD only. Notice, Base has been extended to B to get the height.

law258 · Answer

This question tests your understanding of similar triangles.

You should derive the following equation using this concept:

(1/2)(9)(AB) - (1/2)(4)(AB) = 10
AB(5/2) = 10
AB = 4

Therefore, we know the rectangle is a 4x9. Area = 36

rikson · Answer

Hi,,,lawiniecke,,,I have doubt that you subtract only ABE from whole,,,but there is another triangle ACD has which you didn't consider,,,so,,what's the reason??.?I mean ,,Area of ACE=10=1/2*9*AB-1/2*4*AB-area of ACE,,,why is it wrong?..Pls,,,,

kanusha · Answer

Area of a triangle ACE = 10
Area = bh/2
b = 5
10 = 5xh/2
h = 4
Now, Rectangle length = 4, width = 9(4+5)
Area = 4x9 = 36
C

KrishnakumarKA1 · Answer

Area of triangle ACE = ½ *EC *AB 
or 10 = ½ * 5*AB 
or AB =4 BC =9. 
Area of rectangle = 9*4 
= 36. Option C

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In the figure, ABCD is a rectangle, and the area of triangle ACE is 10

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In the figure, ABCD is a rectangle, and the area of triangle ACE is 10

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