If the diagonal of a rectangle is 19cm long and its perimeter is 50 cm. Find the area of the rectang

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18 Dec 2018 Area

If the diagonal of a rectangle is 19cm long and its perimeter is 50 cm. Find the area of the rectangle in sq. cm.

OPtion

1) 264
2) 280
3) 140
4) 160
5) 132
6) 144
7) 288
8) 150
9) 130
10) None of these

Solution

Let length = x and breadth = y then

2(x+y) = 50 => x+y = 25
x²+y² = 19² = 361
now (x+y)² = 25²
=> x²+y²+2xy= 625
=> 361 + 2xy = 625
=> xy = 132
area = xy = 132 sq.cm

Option 5)

Correct Option: 5 Best Solution (7)

Pargat Pal Singh   5 years AGO

if x and y are length and breadth respectively, then
area = xy
x+y = 50/2= 25 cms
x^2+y^2- 19^2= 361
2xy = (x+y)^2-(x^2+y^2) = 625-361= 264
xy =132 sq cms

Like? Yes (4) | No (1)  

G.S.Kantharao   5 years AGO

l+b+d=50
l+b=25
(l+b)^2=25^2
l^2+b^2+2lb=25^2
19^2+2lb=25^2
Lb=(25^2-19^2)/2=44*6/2=132
Right option is 5👈

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AASHRAY AJAY SHARMA   5 years AGO

Perimeter=2(l+b) = 50 => l+b = 25 cm
Diagonal =(l^2+b^2)^1/2 = 19 => l^2+b^2 = 19^2
Therefore, (l+b)^2 = l^2+b^2 + 2lb
25^2 = 19^2 +2(lb)
lb= (25^2 - 19^2)/2 = 132 sqcm.

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Devendra Marghade   5 years AGO

Let sides of a rectangle be x and y, then
Perimeter=2(x+y)=50 => x+y=25 ---(i) and
Diagonal^2=x^2+y^2 =19^2
=> x^2+y^2=361 ---(ii)
Now to calculate area we need xy.
As (x+y)^2=x^2+y^2+2xy
Substituting values from equation (i) and (ii), we get
25^2 = 361 + 2xy
=> 2xy = 264 or xy=132 sq. cm.
Option 5)

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Kariamal   5 years AGO

2(l+b)=50
l+b=25
l^2+b^2=19^2=361
(l+b)^2=l^2+b^2+2lb
625=361+2lb
lb=132

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SAYAN CHATTERJEE   5 years AGO

a^2+b^2= 19^2
a+b=25
on. solving, we get, a= 17.42, b= (25-17.42)= 7.58.
Area= ab= 132.
Option 5.

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RAMADURAI NATESAN   5 years AGO

2(l+b)=50. l+b=25. d sq =lsq+bsq.=19sq. =361
(l+b)sq.=lsq.+bsq.+2lb.=625.
2lb =625 - 361 =264. Area = lb = 132

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