Area - Study Mode

[#131] What will be the area of 4 metres high wall on all four sides of a rectangular hall having perimeter 64 m ?
Correct Answer

(A) 256 m 2

Explanation

Solution: Perimeter = 64 m ⇒ 2(l + b) = 64 ∴ Area of 4 walls = 2(l + b) × h = (64 × 4) m 2 = 256 m 2

[#132] The altitude of an equilateral triangle of side $$2sqrt 3 $$ cm is :
Correct Answer

(D) 3 cm

Explanation

Solution: Let ABC be the equilateral triangle and AD be the altitude on base BC In an equilateral triangle, the altitude and the median coincide. So, BC = DC = $$left( {frac{{2sqrt 3 }}{2}}
ight)$$ cm = $$sqrt 3 $$ cm Let the length of the altitude AD be x cm Then, in right angled ΔADB, AB 2 = AD 2 + BD 2 ⇒ $${left( {2sqrt 3 }
ight)^2}$$xa0 = x 2 + $${left( {sqrt 3 }
ight)^2}$$ ⇒ x 2 = (12 - 3) ⇒ x 2 = 9 ⇒ x = 3 cm

[#133] One of the diagonals of a rhombus is double the other diagonal. Its area is 25 sq. cm. The sum of the diagonal is ?
Correct Answer

(C) 15 cm

Explanation

Solution: $$eqalign{
& Leftrightarrow frac{1}{2}{d_1} imes 2{d_1} = 25 cr
& Leftrightarrow d_1^2 = 25 cr
& Leftrightarrow {d_1} = 5 cr} $$ ∴ Sum of lengths of diagonals = (5 + 10) cm = 15 cm

[#134] Cost of fencing a circular plot at the rate of Rs. 15 per metre is Rs. 3300. What will be the cost of flooring the plot at the rate of Rs. 100 per square metre ?
Correct Answer

(C) Rs. 385000

Explanation

Solution: Circumference of the plot : $$eqalign{
& = left( {frac{{3300}}{{15}}}
ight)m cr
& = 220,m cr
& Rightarrow 2pi R = 220 cr
& Rightarrow R = frac{{220 imes 7}}{{2 imes 22}} cr
& Rightarrow R = 35,m cr} $$ Area of the plot : $$eqalign{
& = left( {frac{{22}}{7} imes 35 imes 35}
ight){m^2} cr
& = 3850,{m^2} cr} $$ ∴ Cost of flooring : $$eqalign{
& = { ext{Rs}}{ ext{.}}left( {3850 imes 100}
ight) cr
& = { ext{Rs}}{ ext{. 385000}} cr} $$

[#135] The ratio of the circumferences of two circles is 2 : 3. What is the ratio of their areas ?
Correct Answer

(B) 4 : 9

Explanation

Solution: $$eqalign{
& Rightarrow frac{{2pi {R_1}}}{{2pi {R_2}}} = frac{2}{3} cr
& Rightarrow frac{{{R_1}}}{{{R_2}}} = frac{2}{3} cr
& Rightarrow frac{{pi R_1^2}}{{pi R_2^2}} = {left( {frac{2}{3}}
ight)^2} cr
& Rightarrow frac{{pi R_1^2}}{{pi R_2^2}} = frac{4}{9} ext{ or } 4:9 cr} $$