Area of a rectangle is equal to the area of the circle whose radius is 21 cms. If the length and the breadth of the rectangle are in the ratio of 14 : 11 respectively, what is its perimeter ?
A horse is tethered to a peg with a 14 meter long rope at the corner of a 40 meter long and 24 meter wide rectangular grass-field. What area of the field will the horse graze?
(a) \(\displaystyle 154{{m}^{2}}\)
(b) \(\displaystyle 308{{m}^{2}}\)
(c) \(\displaystyle 240{{m}^{2}}\)
(d) \(\displaystyle 480{{m}^{2}}\)
(e) None of these
Solution: (a)
Required area = \(\displaystyle \frac{1}{4}\times \pi {{R}^{2}}\)
The length of a rectangular field is double its width. Inside the field there is a square-shaped pond 8 m long. If the area of the pond is 1/8 of the area of the field, what is the length of the field?
(a) 32 m
(b) 16 m
(c) 64 m
(d) 20 m
(e) None of these
Solution: (a)
Let width of the field = b m
\(\displaystyle \Rightarrow \) Length = 2 b m
Now, area of rectangular field = \(\displaystyle 2b\times b\)= \(\displaystyle 2{{b}^{2}}\)
Area of square shaped pond = \(\displaystyle 8\times 8=64\)
Therefore, Length of the field = \(\displaystyle 16\times 2=32m\)
The area of a right-angled triangle is two-thirds of the area of a rectangle. The base of the triangle is 80 percent of the breadth of the rectangle. If the perimeter of the rectangle is 200 cm, what is the height of the triangle?
(a) 20 cm
(b) 30 cm
(c) 15 cm
(d) Data inadequate
(e) None of these
Solution: (d)
Let the base and height of triangle, and length and breadth of rectangle be L and h, and \(\displaystyle {{L}_{1}}and{{b}_{1}}\) respectively. Then, \(\displaystyle \frac{1}{2}\times L\times h=\frac{2}{3}\times {{L}_{1}}\times {{b}_{1}}\) …(i)
\(\displaystyle L=\frac{4}{5}{{b}_{1}}\) …(ii)
And \(\displaystyle {{L}_{1}}+{{b}_{1}}=100\) …(iii)
In the above we have three equations and four unknowns. Hence the value of ‘h’ can’t be determined.
