Question

We all know that a kite is basically a sheet of thin paper stretched on a wooden frame. Ram had one such kite as shown in the figure below. Unfortunately the central wooden stick (ROT) broke. What length of wood would he require to replace it?

• A. 32 cm
• B. 42 cm
• C. 52 cm
• D. 72 cm

Answer 1

The correct option is D

72 cm

$In\Delta ROS,$
$O{R}^2+O{S}^2=R{S}^2$
$O{R}^2=R{S}^2-O{S}^2$
$={\left(50cm\right)}^2-{\left(40cm\right)}^2$
$=2500c{m}^2-1600c{m}^2$
$=900c{m}^2$
$OR=\sqrt{900}c{m}^2=30cm.$
$In\Delta SOT,$
$O{T}^2+O{S}^2=S{T}^2$
$O{T}^2=S{T}^2-O{S}^2$
$={\left(58cm\right)}^2-{\left(40cm\right)}^2$
$=3364c{m}^2-1600c{m}^2$
$OT=\sqrt{1764}c{m}^2=42cm.1764$
The wooden stick equals ROT, i.e., RO + OT = 30 cm + 42 cm = 72 cm.