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Question 62
The diagonal of a rectangle field is 15 m and its area is 108 $$m^2$$ . What is the cost of fencing the field at ₹50.50 per m?
Solution
Area of a rectangle=l*b
lb=108
Diagonal of a rectangle=$$\sqrt{l^{2}+b^{2}}\sqrt{l^{2}+b^{2}}$$
225=$$l^{2}+b^{2}$$
225+216=$$l^{2}+b^{2}+2lb$$
441=$$(l+b)^{2}$$
l+b=21
l+(108/l)=21
$$l^{2}+108$$=$$21l$$
$$l^{2}-21l+108$$=0
$$l^{2}-12l-9l+108$$=0
l(l-12)-9(l-12)=0
(l-9)(l-12)=0
l=9 cm b=12cm
Perimeter of rectangle=2(l+b)
=42 cm
Cost of fencing=42*50.5
=Rs 2121
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