Rectangle and Squares
Questions
Q1.
Find the diagonal of a Rectangle whose sides are 12 m and 5 m .
Solution.
Length of the diagonal = √ (length2 + breadth2)
= √(122 + 52)
=13 m
Solution
Q2.
The side of square is 4 m . find the diagonal of the square .
diagonal = a√2
d = 4√2
Solution
Q3.
The diagonal of square is 6m , find the area of square .
Solution.
Area = (62/2) = 36/2 = 18
Solution
Q4.
The ratio of area of 2 squares is 16:25 , find the ratio of their perimeter .
Solution.
4:5
Note : ratio of perimetres = √a1 : √a2 . if a1 : a2
are the
ratio of their area .
Solution
Q5.
If the lenght of square is increases by 20% then find the increase in area (in percentage).
Solution.
Percentage change = 2x +
x2/100
= 44%
Solution
Q6.
The length and breadth of a Rectangle become double, find the percentage change in area ?
Solution.
In this case % change = (mn - 1) x 100%
= (2 x 2 - 1) x100%
= 300%
Solution
Q7.
Area of square is 882 m2 find its diagonal.
Solution.
Area = d2/2
d = 42 m
Solution
Q8.
If the side of the square is increases by 50% , then find the ratio of new square and given square .
Solution.
In this case area will increases 125%
desired ratio = 225:100
9:4
Solution
Q9.
Find the ratio of area of a square and equilateral triangle each having side a .
Solution.
4:√3
Solution
Q10.
Find the perimeter of square , whose sum of diagonals are 144 cm .
Solution.
2d = 144 (given)
d = 72
a√2 = 72
a = 72/√2
perimeter of square = 4a = 288/√2 = 144√2 cm
Solution
