Question

*The area of a square and a rectangle are in the ratio 2:3. If the side length of the square is the same as the breadth of the rectangle, what is the ratio of the perimeter of the square to the perimeter of the rectangle?*

1️⃣ 4:5
2️⃣ 2:3
3️⃣ 3:2
4️⃣ 5:4​

Answer 1

Answer:

ratio is 4:5 .

Step-by-step explanation:

Given :-

• area of square : area of rectangle = 2:3
• length of square side = breadth of rectangle .

To find :- Ratio of perimeter of square : perimeter of rectangle .

Solution :-

Step 1) Let $A_1$ = area of square , $A_2$ = area of rectangle

            $l =$  side length of square , $h , b$ = length and breadth of rectangle .

Step 2) Given that , $\frac{A_1}{A_2} = \frac{2}{3}$ --- (1)

We know that , $A_1 = l^2$ , $A_2 = h*b$ --- (2)

therefore , in eqn. (1)

$\frac{l^2}{h*b} = \frac{2}{3}$  ---- (2)

also , $l=b$

thus , $= \frac{l^2}{l*h} = \frac{2}{3}\\= \frac{l}{h} = \frac{2}{3}$

we get ,  $h = \frac{3l}{2}$ ----- (3)

Step 3) Perimeter ratio ,

Let $P_1$ = perimeter of square  , $P_2$ = perimeter of rectangle .

therefore ,

$\frac{P_1}{P_2} = ?$

We know , $P_1 = 4 l \\and \\P_2 = 2 *(h + b)$

$\frac{P_1}{P_2} = \frac{4 l}{2(h+b) }$

$= \frac{P_1}{P_2} = \frac{4 l }{2*(\frac{3 l}{2} +l )}\\= \frac{P_1}{P_2} = \frac{4 l }{5 l } \\= \frac{P_1}{P_2} = \frac{4}{5}$

Therefore , ratio is 4:5

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