Question

the adjacent sides of a rectangle are in the ratio 4 ratio 3 and its perimeter is 42 centimetre find the length of its diagonal.

Answer 1

Given, the adjacent sides of the rectangle are in the ratio 3:4.
Let the two sides of the rectangle be 3x and 4x respectively.
So, Perimeter of the rectangle = 2(l + b) = 2(3x + 4x) = 42 cm
                                                                         7x = 21 Hence, x = 3
Length = 4x3 = 12cm, Breadth = 3x3 = 9cm
By applying Pythagoras Theorem,
Diagonal of the rectangle = √(9)² + (12)²
                                            = √225 = 15cm, which is the answer.

Answer 2

Let the length of the rectangle be 4x and breadth be 3x...
Now perimeter=42 cm
Perimeter of rectangle= 2(l +b)
42=2(4x+3x)
21=7x
X=3
So length =12 cm and breadth=9cm
Now using pythagoras theorem...
(12*12)+(9*9) = diagonal*diagonal
144
$\sqrt{144 + 81} = diagonal$
So diagonal = 15 cm...


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