If the diagonal of a rectangle is 18cm long and its perimeter is 44 cm. Find the area of the rectang

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24 Apr 2019 Area

If the diagonal of a rectangle is 18cm long and its perimeter is 44 cm. Find the area of the rectangle.

OPtion

1) 70 sq.cm
2) 76 sq.cm
3) 78 sq.cm
4) 74 sq.cm
5) 75 sq.cm
6) 72 sq.cm
7) 80 sq.cm
8) 86 sq.cm
9) 94 sq.cm
10) None of these

Solution

Let length = x and breadth = y then

2(x+y) = 44 => x+y = 22
x²+y² = 18² = 324
now (x+y)² = 22²
=> x²+y²+2xy= 484
=> 324 + 2xy = 484
=> xy = 80

Area = xy = 80 sq.cm

Correct Option: 7 Best Solution (5)

G.S.Kantharao   5 years AGO

2(l+b)=44=>l+b=22
l^2+b^2+2lb=484
d^2+2lb=484=>2lb=484-18^2
=484-324=160
Area=lb=160/2=80sq.cm
Right option is 7👈

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Devendra Marghade   5 years AGO

Let sides of a rectangle be a & b cm respectively, then
Perimeter=2(a+b)
44 = 2(a+b) => a+b = 22 ---(i)
Diagonal^2 = a^2 + b^2
18^2 = a^2 + b^2 => a^2 + b^2 = 324 ---(ii)
Now, (a+b)^2 = a^2 + b^2 + 2ab
Substituting values from (i) & (ii), 22^2 = 324 + 2ab
2ab = 160
ab = 80 sq. cm = Area of a rectangle
Option 7)

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Varun   5 years AGO

Pythagoras theorem
(l+b)^2=l^2+b^2+2lb
Perimeter = 2(l+b)= 44 => l+b=22
Diagonal = 18 = l^2+b^2
=> lb=80 = option (7)

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suryanarayana   5 years AGO

Diagonal is 18cm
L²+b²=324
Perimeter is 44cm
L+b=22
Then area of reactangle is lb=80cm²

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Dimple   5 years AGO

l+b = 44/2= 22 cms
l^2+b^2= 18^2=324
solving these eqns, we get,
area= l*b = (22^2-18^2)/2= 80 sq cms

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