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# If the diagonal and the area of a rectangle are 25 units and 168 unit

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Math Expert
Joined: 02 Sep 2009
Posts: 59721
If the diagonal and the area of a rectangle are 25 units and 168 unit  [#permalink]

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12 Nov 2019, 03:30
00:00

Difficulty:

55% (hard)

Question Stats:

65% (02:24) correct 35% (01:58) wrong based on 37 sessions

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If the diagonal and the area of a rectangle are 25 units and 168 unit^2 respectively, what is the length of the larger side of the rectangle?

A. 12
B. 21
C. 24
D. 25
E. 38

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_________________
Intern
Joined: 02 Nov 2017
Posts: 32
Location: India
GPA: 3.87
Re: If the diagonal and the area of a rectangle are 25 units and 168 unit  [#permalink]

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12 Nov 2019, 04:03
Let the length and breadth of the rectangle be ‘l’ and ‘b’ respectively.

(Diagonal)^2 = l^2 + b^2

or, l^2 + b^2 = 25^2 = 625 ………………….(1)

Area of the rectangle = l x b = 168 ……………. (2)

Now, (l + b)^2 = l^2 + b^2 + 2 x l x b = 625 + 2 x 168 = 961

or, l + b = 31 ……………. (3)

Similarly, (l - b)^2 = l^2 + b^2 - 2 x l x b = 625 - 2 x 168 = 289

or, l - b = 17 …………… (4)

Solving (3) and (4), we get :

l = 24 cm
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Joined: 18 Aug 2017
Posts: 5483
Location: India
Concentration: Sustainability, Marketing
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WE: Marketing (Energy and Utilities)
Re: If the diagonal and the area of a rectangle are 25 units and 168 unit  [#permalink]

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12 Nov 2019, 04:03
168 = 2^3*4*7
digonal = 25 ;
larger side ; 24^2+7^2 = 625 ; √625 = 25
IMO C

Bunuel wrote:
If the diagonal and the area of a rectangle are 25 units and 168 unit^2 respectively, what is the length of the larger side of the rectangle?

A. 12
B. 21
C. 24
D. 25
E. 38

Are You Up For the Challenge: 700 Level Questions
Manager
Joined: 10 Dec 2017
Posts: 151
Location: India
If the diagonal and the area of a rectangle are 25 units and 168 unit  [#permalink]

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12 Nov 2019, 05:20
Bunuel wrote:
If the diagonal and the area of a rectangle are 25 units and 168 unit^2 respectively, what is the length of the larger side of the rectangle?

A. 12
B. 21
C. 24
D. 25
E. 38

Are You Up For the Challenge: 700 Level Questions

Since
$$25^2=X^2+Y^2$$
and product is 168
last digit is 8
check options
24*7
Perfect
C
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3158
Re: If the diagonal and the area of a rectangle are 25 units and 168 unit  [#permalink]

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24 Nov 2019, 21:11

Solution

Given:
• The area of a rectangle = 168 square units
• The length of the diagonal = 25 units

To find:
• The length of the larger side of the rectangle

Approach and Working Out:
• Given,
o l * b = 168
o $$l^2 + b^2 = 25^2$$

• By simple observation, we can write 168 = 24 * 7 and $$25^2 = 24^2 + 7^2$$
• Therefore, the length of the rectangle = 24 units

Hence, the correct answer is Option C.

_________________
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3158
Re: If the diagonal and the area of a rectangle are 25 units and 168 unit  [#permalink]

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25 Nov 2019, 20:52

Solution

Given
• The diagonal and the area of a rectangle are 25 units and 168 unit^2 respectively

To find
• The length of the larger side of the rectangle

Approach and Working out

Let a and b are the sides of the rectangle.
• a^2 + b^2 = 25^2 = 625
• ab = 168

(a + b)^2 = a^2 + b^2 + 2ab = 625 + 2 * 168 = 625 +336 = 961
• (a + b) = 31
(a - b)^2 = a^2 + b^2 - 2ab = 625 +-2 * 168 = 625 - 336 = 289
• (a - b) = 17

2a = 48, a = 24
• b = 7

Thus, option C is the correct answer.
_________________
Re: If the diagonal and the area of a rectangle are 25 units and 168 unit   [#permalink] 25 Nov 2019, 20:52
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