Area - Study Mode

[#216] A boundary wall around a rectangular plot is constructed at a total cost of Rs. 46000 at the rate of Rs. 200 per metre. What is the area of the plot if the respective ratio between the breadth and the length of the plot is 10 : 13 ? (in sq. metre)
Correct Answer

(B) 3250 sq. m 2

Explanation

Solution: Total cost to construct a boundary wall around a rectangular plot = Rs. 46000 Rate of construction per metre = Rs. 200 Perimeter of rectangular plot = $$frac{46000}{200}$$ xa0 = 230 m Let the length and breadth of rectangular plot be 13x metre and 10x metre respectively $$eqalign{
& herefore 2left( {13x + 10x}
ight) = 230 cr
& Rightarrow 2 imes 23x = 230 cr
& Rightarrow x = frac{{230}}{{2 imes 23}} cr
& Rightarrow x = 5 cr} $$ ∴ Length = 13 × 5 = 65 cm Breadth = 10 × 5 = 50 m ∴ Area of plot = 65 × 50 = 3250 sq. m 2

[#217] A rectangle of certain dimension is chopped off from one corner of a larger rectangle as shown. AB = 8 cm and BC = 4 cm. The perimeter of the figure ABCPQRA (in cm) is :
Correct Answer

(A) 24 cm

Explanation

Solution: Required perimeter : = (AB + BC + CP + PQ + QR + RA) = AB + BC + (CP + QR) + (PQ + RA) = AB + BC + AB + BC = [2 (8 + 4)] cm = 24 cm

[#218] A rectangular field has dimensions 25 m by 15 m. Two mutually perpendicular passages, 2 m wide have been left in its central part and grass has been grown in rest of the field. The area (in sq. metres) under the grass is :
Correct Answer

(B) 299 m 2

Explanation

Solution: Area of the field : = (25 × 15) m 2 = 375 m 2 Area of the passages : = (25 × 2 + 15 × 2 - 2 × 2) m 2 = 76 m 2 Area under grass : = (375 - 76) m 2 = 299 m 2

[#219] A room is $$12frac{1}{4}$$ m long and 7 m wide. The maximum length of a square tile to fill the floor of the room with whole number of tiles should be :
Correct Answer

(C) 175 m

Explanation

Solution: Length of largest tile : = H.C.F. of $$12frac{1}{4}$$ m and 7 m = H.C.F. of 12.25 m and 7 m = H.C.F. of 1225 cm and 700 cm = 175 cm

[#220] If the area of a square increase by 69%, then the side of the square increases by :
Correct Answer

(B) 30%

Explanation

Solution: Le original area = 100 cm 2 Then, new area = 169 cm 2 ⇒ Original side = 10 cm New side = 13 cm Increase on 10 cm = 3 cm Increase % : $$eqalign{
& = left( {frac{3}{{10}} imes 100}
ight)\% cr
& = 30\% cr} $$