a) 36тИЪ3 cm^2;
b) 80тИЪ3 cm^2;
c) 48тИЪ813 cm^2;
c)┬а64тИЪ3 cm^2;
Explanation:
Area of an equilateral triangle = тИЪ3/4 S^2┬а
If S = 16, Area of triangle = тИЪ3/4 * 16 * 16 =┬а64тИЪ3 cm^2;2.┬аIf the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area?
a)┬а140 cm^2
b)┬а120 cm^2
c) 80 cm^2
d) 60 cm^2
Explanation:
The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle = 1/2 * 24 * 10 = 120 cm^23.┬аThe perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
a)┬а35 cm^2
b) 42┬аcm^2
c) 49┬аcm^2
d) 63┬аcm^2
Explanation:
Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.Area of triangle = 2.5 * 28/2 = 35 cm^2
4.┬аFind the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm.
a)┬а270 cm^2
b)┬а275 cm^2
c)┬а280 cm^2
d)┬а285 cm^2
Explanation:
Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (15) = 285 cm^2
5.┬аFind the area of a parallelogram with base 24 cm and height 16 cm.
a)┬а384 cm^2
b)┬а394 cm^2
c)┬а364 cm^2
d)┬а344 cm^2
Explanation:
Area of a parallelogram = base * height = 24 * 16 = 384 cm^2
6.┬аThe ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm.
Find the ratio of the breadth and the area of the rectangle?
b) 1 : 48
c) 1 : 84
d).┬а1 : 68
┬а
Explanation:
Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 691212x^2┬а= 6912┬а
x^2┬а= 576 = 4 * 144 = 2^2┬а* 12^2┬а(x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x^2┬а= 1 : 4x = 1: 96.
7.┬аThe area of the square formed on the diagonal of a rectangle as its side is 108 (1/3) % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
a) 3m.
b) 6m.
c) 4m.
d)┬а2m.
Explanation:
Let the sides of the rectangle be l and b respectively.
From the given data,┬а(тИЪl^2┬а+ b^2) = (1 + 108 1/3 %)lb┬а
=> l^2┬а+ b^2┬а= (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l^2┬а+ b^2)/lb = 25/12┬а
12(l^2┬а+ b^2) = 25lb┬а
Adding 24lb on both sides┬а
12l^2┬а+ 12b^2┬а+ 24lb = 49lb┬а
12(l^2┬а+ b^2┬а+ 2lb) = 49lb┬а
but 2(l + b) = 28 => l + b = 14┬а
12(l + b)^2┬а= 49lb┬а
=> 12(14)^2┬а= 49lb┬а
=> lb = 48┬а
Since l + b = 14, l = 8 and b = 6┬а
l - b = 8 - 6 = 2m.
8.┬аThe length of a rectangular plot is thrice its breadth.
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If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?a)┬а8.5 m
b) 17 m
c) 34 m
d)┬а51 m
┬а
Explanation:
Let the breadth of the plot be b m.
Length of the plot = 3 b m(3b)(b) = 867
3b^2┬а= 867┬а
b2┬а= 289 = 172┬а(b > 0)
b = 17 m.
9.The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?
a)┬а27 m
b).┬а24 m
c).┬а18 m
d).┬а21 m
┬а
Explanation:
Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3bArea of the floor = 324/3 = 108 sq m
l b = 108 i.e., l * l/3 = 108
l^2┬а= 324 => l = 18.
10.┬аAn order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?
a)┬аRs. 4052.40
b)┬аRs. 4062.40
c)┬аRs. 4082.40
d)┬аRs. 4072.40
Explanation:
Length of the first carpet = (1.44)(6) = 8.64 cm
Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m
Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40