Question

Ratio of a diagonal of a rectangle to its smaller side is 5 : 2. Find the ratio of its

longer side to the smaller side​

Answer 1

$\textbf{Given:}$

$\textsf{Ratio of diagonal of rectangle to its smaller side is 5:2}$

$\textbf{To find:}$

$\textsf{Ratio of its longer side to the smaller side}$

$\textbf{Solution:}$

$\textsf{Let l,b and h be the length, breadth and diagonal of the given rectangle}$

$\textsf{As per given data,}$

$\mathsf{d:b=5:2}$

$\implies\mathsf{d=5k,\;\;b=2k}$

$\mathsf{But,\;d^2=l^2+b^2}$

$\mathsf{(5k)^2=l^2+(2k)^2}$

$\mathsf{25k^2=l^2+4k^2}$

$\mathsf{25k^2-4k^2=l^2}$

$\mathsf{21k^2=l^2}$

$\implies\mathsf{l=\sqrt{21}k}$

$\mathsf{Now,}$

$\mathsf{l:b}$

$\mathsf{=\sqrt{21}k:2k}$

$\mathsf{=\sqrt{21}:2}$

$\therefore\boxed{\mathsf{l:b=\sqrt{21}:2}}$

Answer 2

Step-by-step explanation:

$\textbf{Given:}:$

$\textsf{Ratio of diagonal of rectangle to its smaller side is 5:2}$

$\textbf{To find:}:$

$\textsf{Ratio of its longer side to the smaller side}$

$\textbf{Solution:}:$

$\textsf{Let l,b and h be the length, breadth and diagonal of the given rectangle}$

$\textsf{As/ per /given /data,},$

$\mathsf{d:b=5:2}d:b=5:2$

$\implies\mathbb{d=5k\;b=2k⟹d=5k,b=2k$

$\mathsf{But,\;d^2=l^2+b^2}But,d 2=l2+b 2$

$\mathsf{(5k)^2=l^2+(2k)^2}(5k)2=l 2+(2k) 2$

$\mathsf{25k^2=l^2+4k^2}25k 2 =l 2+4k 2$

$\mathsf{25k^2-4k^2=l^2}25k 2−4k2=l 2$

$\mathsf{21k^2=l^2}21k 2 =l2$

$\implies\mathsf{l=\sqrt{21}k}⟹l=21 k$

$\mathsf{Now,},$

$\mathsf{l:b}l:b$

$\mathsf{=\sqrt{21}k:2k}= 21k:2k$

$\mathsf{=\sqrt{21}:2}= 21:2$

$\therefore\boxed{\mathsf{l:b=\sqrt{21}2}}∴$

$l:b= 21 :2$