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# The figure shows a rectangle with a triangle inscribed in it

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Senior PS Moderator
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The figure shows a rectangle with a triangle inscribed in it  [#permalink]

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24 Nov 2018, 23:34
1
2
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Difficulty:

45% (medium)

Question Stats:

56% (00:52) correct 44% (01:15) wrong based on 38 sessions

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Geometry.JPG [ 4.33 KiB | Viewed 519 times ]

The figure shows a rectangle with a triangle inscribed in it. What is the area of the rectangle?

1. The area of the shaded region in 40.
2. The area of the non-shaded region is 40.

Source: Experts Global

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Re: The figure shows a rectangle with a triangle inscribed in it  [#permalink]

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24 Nov 2018, 23:46
(1): 1/2*w*l=40, so w*l (area of rect.) is 80. sufficient.
(2): 1/2(wa)+1/2(wb)=40; a+b=l -> w(a+b)=w*l=80; so, sufficient.

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Re: The figure shows a rectangle with a triangle inscribed in it  [#permalink]

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24 Nov 2018, 23:49
pushpitkc wrote:
Attachment:
Geometry.JPG

The figure shows a rectangle with a triangle inscribed in it. What is the area of the rectangle?

1. The area of the shaded region in 40.
2. The area of the non-shaded region is 40.

Source: Experts Global

Rectangle with a triangle inscribed in it

Area of triangle will 1/2 of the area of Rectangle

Bcoz Area of triangle =(1/2)bh and area of rectangle =l*b

Hence here b=l

therefore area of triangle will 1/2 of the area of Rectangle

1. The area of the shaded region in 40.

Here Area of triangle =40

Area of rectangle =80

2. The area of the non-shaded region is 40.

Area of rectangle =80

Hence D
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Re: The figure shows a rectangle with a triangle inscribed in it  [#permalink]

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24 Nov 2018, 23:52
pushpitkc wrote:
Attachment:
Geometry.JPG

The figure shows a rectangle with a triangle inscribed in it. What is the area of the rectangle?

1. The area of the shaded region in 40.
2. The area of the non-shaded region is 40.

Source: Experts Global

Now area of rectangle is L*B..
the area of shaded region is $$\frac{1}{2}*L*H$$, here height is nothing but the B of rectangle and ofcourse the Ls are same in each case..Thus area = $$\frac{1}{2}*L*B$$

so area of rectangle is HALF the area of shaded region OR the area of shaded region is the area of non-shaded region

Let us see the statements now..

1. The area of the shaded region in 40.
so area of rectangle is twice of 40 = 2*40=80
sufficient

2. The area of the non-shaded region is 40.
so area of rectangle is twice of 40 = 2*40=80
sufficient

D
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Re: The figure shows a rectangle with a triangle inscribed in it   [#permalink] 24 Nov 2018, 23:52
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