The Triangles and Its Properties — MATHS STD 7 — Question

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

Let the breadth of a rectangle be $xcm.$
In right angled $\triangle\text{ABC},$
$⇒ (AC)^2 = (AB)^2 + (BC)^2$
$⇒ (BC)^2 = (AC)^2 + (AB)^2$ [by pythagoras theoram]
$⇒ x^2 = (61)^2 - (60)^2 = 3721 - 3600 = 121$
$\Rightarrow \ \text{x}=\sqrt{121}=11\text{cm}$
$\therefore$ Breadth of rectangle $= 11cm$ and length of rectangle $= 60cm.$
Now, perimeter of rectangle $= 2(l + b)$
$= 2(60 + 11) = 2 × 71$
$= 142cm.$