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12 Nov 2019, 03:30
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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
Are You Up For the Challenge: 700 Level Questions
A. 12
B. 21
C. 24
D. 25
E. 38
Are You Up For the Challenge: 700 Level Questions
indu1954
Joined: 02 Nov 2017
Last visit: 23 Feb 2020
Posts: 29
Own Kudos:
Given Kudos: 22
Location: India
Schools: UVA Darden Tepper Babson '21 Johnson '21 Rotman '21 Booth '22
GPA: 3.87
12 Nov 2019, 04:03
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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
(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
12 Nov 2019, 04:03
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168 = 2^3*4*7
digonal = 25 ;
larger side ; 24^2+7^2 = 625 ; √625 = 25
IMO C
digonal = 25 ;
larger side ; 24^2+7^2 = 625 ; √625 = 25
IMO C
Bunuel
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
A. 12
B. 21
C. 24
D. 25
E. 38
Are You Up For the Challenge: 700 Level Questions
