Question

The perimeters of two squares are in the ratio 8:15, find the ratio between the
lengths of their sides.
​

Answer 1

$\Large\underline{\underline{\sf \red{Given}:}}$

• Ratio of perimeter of two square = 8:15

$\Large\underline{\underline{\sf \red{To\:Find}:}}$

• Ratio between the lengths of their sides = ?

$\Large\underline{\underline{\sf \green{Formula\:Used}:}}$

${\boxed{\sf \red{Perimeter\:of\:square(P)=4×side} }}$

$\Large\underline{\underline{\sf \green{Solution}:}}$

Let ,

Perimeter of first square = 8x

and , perimeter of second square is = 15x

____________________

Side of first square = $\sf{\dfrac{Perimeter}{4}}$

$\implies{\sf \dfrac{8x}{4}}$

__________________

Side of second square = $\sf{\dfrac{Perimeter}{4}}$

$\implies{\sf \dfrac{15x}{4} }$

________________

Ratio of sides of square :-

$\implies{\sf \dfrac{Side\:of\:first\: Square}{Side\:of\:second\: Square}=\dfrac{8x/4}{15x/4}}$

$\implies{\sf \dfrac{8}{15} }$

$\Large\underline{\underline{\sf \green{Answer}:}}$

⛬ Ratio of sides of squares is 8:15

Answer 2

$\Large\underline{\underline{\sf{Given}:}}$

• Perimeter of Two squares ratio = 8:15 .

$\large\tt{Question:-}$

• Ratio between their sides .

${\large\bf{\mid{\overline{\underline{Concept\:Used}}}\mid}}$

• The ratio of perimeter of squares is same as ratio of their sides ....

$\large\tt{Proof:-}$

Let two Squares have sides be :- a1 and a2 .

Perimeter of Square with side a1 = 4× side = 4a1

Perimeter of Square with side a2 = 4 × side = 4a2 .

Ratio of their Perimeter = 4a1 : 4a2 = $\red{\bold{a1:a2}}$

$\Large\underline{\underline{\sf{Proved}}}$

_________________________________

Hence, Ratio of sides with perimeter 8:15 will be same.

so, side ratio is = $\bold{\red{8:15}}$