Question

Question 16

The perimeter of the rectangle whose length is 60 cm and a diagonal is 61 cm is

a) 120 cm
b) 122 cm
c) 71 cm
d) 142 cm

Answer 1

Given, length of rectangle = 60 cm and its diagonal = 61 cm.

Let the breadth of a rectangle be x cm
In right angled $\Delta ABC$
$\Rightarrow (AC{)}^2=(AB{)}^2+(BC{)}^2$
$\Rightarrow (BC{)}^2=(AC{)}^2-(AB{)}^2$ [By Pythagoras theorem]
$\Rightarrow x^2=(61{)}^2-(60{)}^2=3721-3600=121\Rightarrow x=\sqrt{121}=11cm$
$\therefore$ Breadth of rectangle = 11 cm and length of rectangle = 60 cm
Now, perimeter of rectangle $=2(l+b)$
$=2(60+11)=2\times 71$
$=142cm$