Question

The dimensions of a park are in the ratio 5 : 2. If the area of the park is 1440 m.sq. Find the
dimensions of the park.
​

Answer 1

$\large{\sf{\green{\underline{\underline{✝\:GIVEN\:✝}}}}}$

The dimensions of a park are in the ratio 5:2.

$\large\bold{\sf{Area\: of\: the\: park\: =\:1440{m}^{2}}}$

$\large{\sf{\green{\underline{\underline{✝\:To\:Find\:✝}}}}}$

The dimensions of the park.

$\large{\sf{\green{\underline{\underline{✝\:SOLUTION\:✝}}}}}$

As we know that formula of area of rectangle is = length × breadth.

$\large{\sf{Let\: the\: dimensions \:be\: 5x, \:2x.}}$

$\large\blue{\sf{According\: to\: the\: question,}}$

$\large\Longrightarrow{\sf{5x×2x=1440}}$

$\large\Longrightarrow{\sf{10{x}^{2}=1440}}$

$\large\Longrightarrow{\sf{{x}^{2}=\frac{1440}{10}}}$

By square rooting both the sides,

$\large\Longrightarrow{\sf{x=\sqrt{144}}}$

$\large\therefore\boxed{\sf{x=\frac{+}{-}12}}$

So the dimensions are:-

$\large{\sf{5x=5×12=60\: m}}$

$\large{\sf{5x=2×12=24\:m}}$

$\large\boxed{\sf{\pink{The\: dimensions\: are\: 60\: m, \:24\: m.}}}$