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# The area of the parallelogram in the figure above is 40. If QR = 10 an

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The area of the parallelogram in the figure above is 40. If QR = 10 an [#permalink]

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27 Sep 2017, 04:48
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The area of the parallelogram in the figure above is 40. If QR = 10 and ST = 7, then the perimeter of the parallelogram is

(A) 30
(B) 36
(C) 40
(D) 45
(E) 50

[Reveal] Spoiler:
Attachment:

2017-09-27_1107_001.png [ 5.33 KiB | Viewed 472 times ]
[Reveal] Spoiler: OA

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Re: The area of the parallelogram in the figure above is 40. If QR = 10 an [#permalink]

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27 Sep 2017, 06:39
Area of parallogram is bh

Here b = QR, h = QT

Area = 40, QR = 10 , So we get QT = 4.

Also ST = 7 => PT = 3.

Now PTQ is right angled triangle , so we get PQ = 5

Perimeter of parallelogram is 10+5+10+5 = 30

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The area of the parallelogram in the figure above is 40. If QR = 10 an [#permalink]

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28 Sep 2017, 09:31
Bunuel wrote:

The area of the parallelogram in the figure above is 40. If QR = 10 and ST = 7, then the perimeter of the parallelogram is

(A) 30
(B) 36
(C) 40
(D) 45
(E) 50

[Reveal] Spoiler:
Attachment:
2017-09-27_1107_001.png

To find perimeter, find the missing length of the parallelogram's short side (PQ)

That side is the hypotenuse of right ∆ PQT. Leg lengths will yield hypotenuse length.

Find one leg's length from area. Find the other leg's length from (side PS - segment ST)

1) Length of one leg from area
Area = bh
b = 10 (= QR and PS)
40 = 10h
h = 4 = leg QT of right ∆ PQT

2) Length of other leg (PT)
PT = (side PS) - (segment ST)
PT length = (10 - 7) = 3

Legs have lengths 3 and 4.
The triangle is a 3-4-5 right triangle, where hypotenuse = short side (PQ) = 5

Perimeter = 10 + 10 + 5 + 5 = 30

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Re: The area of the parallelogram in the figure above is 40. If QR = 10 an [#permalink]

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28 Sep 2017, 14:45
Expert's post
Top Contributor
Bunuel wrote:

The area of the parallelogram in the figure above is 40. If QR = 10 and ST = 7, then the perimeter of the parallelogram is

(A) 30
(B) 36
(C) 40
(D) 45
(E) 50

[Reveal] Spoiler:
Attachment:
2017-09-27_1107_001.png

Since PQRS is a parallelogram, we know that QR = PS, so side PS also as length 10

Next, the area of a parallelogram = (base)(height)
The base has length 10 and we're told the area = 40
So, we get: (10)(height) = 40, which means the height = 4

We're also told that ST = 7

Since PS has length 10, we can conclude that PT has length 3

Now focus on the RIGHT TRIANGLE ∆PQT

When we apply the Pythagorean Theorem, we see that side PQ (the hypotenuse of ∆PQT) has length 5, which means the side opposite PQ (side RS) also has length 5

So, the perimeter of the parallelogram 10 + 5 + 10 + 5 = 30

[Reveal] Spoiler:
A

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Re: The area of the parallelogram in the figure above is 40. If QR = 10 an [#permalink]

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01 Oct 2017, 12:12
Bunuel wrote:

The area of the parallelogram in the figure above is 40. If QR = 10 and ST = 7, then the perimeter of the parallelogram is

(A) 30
(B) 36
(C) 40
(D) 45
(E) 50

We see that QR (or PS) is the base of the parallelogram and QT is the height of the parallelogram; thus:

10(QT) = 40

QT = 4

Since QR = PS = 10, and ST = 7, PT must be 3.

Thus, triangle PQT is a 3-4-5 right triangle and PQ is 5.

Therefore, the perimeter of the parallelogram is 5 x 2 + 10 x 2 = 10 + 20 = 30.

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Re: The area of the parallelogram in the figure above is 40. If QR = 10 an   [#permalink] 01 Oct 2017, 12:12
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