Question

Length of rectangle is 80% of diagonal of square of area 1225, then find area of rectangle if it's perimeter is 94√2.
(a) 1016
(b) 500
(c) 1604
(d) 1064
(e) 625

Answer 1

Answer – 4.1064 m2

Explanation :

S2 = 1225

S = 35

L = 28√2

2(l+b) = 94√2

b = 19√2; area = 4.1064 m2

Answer 2

We know that Square has all it's side equal,let side of square = a units

Area of square

${a}^{2} = 1225 \\ \\ a = \sqrt{1225} \\ \\ a = 35$
length of diagonal

$\sqrt{2} a = 35 \sqrt{2}$
length of rectangle is 80% of length of diagonal of square,length of rectangle

$= \frac{80}{100} \times 35 \sqrt{2} \\ \\ = 28 \sqrt{2}$
perimeter of rectangle

$= > 2(l + b) = 94 \sqrt{2} \\ \\ 2(28 \sqrt{2} + b) = 94 \sqrt{2} \\ \\ (28 \sqrt{2} + b) = 47 \sqrt{2} \\ \\ b = 47 \sqrt{2} - 28 \sqrt{2} \\ \\ b = 19 \sqrt{2}$
Now,we have both length and breadth of rectangle,so area
$= l \times b \\ \\ = 28 \sqrt{2} \times 19 \sqrt{2} \\ \\ = 1064\: {unit}^{2}$
Thus option (D) is correct.

Hope it helps you.