Question

(3)
If each side of square is increased by 50%.
Then what will be ratio of area of new
square to that of area of original square.
(1) 9:4 (2) 5:4 (3) 4:5 (4) 4:9​

Answer 1

$\underline{\sf\ Solution:-}$

CASE I

Let the side of square be a

We know that

$\underline{\sf\ Area\ of\ square\ = side^2}\\ \\ \\ :\implies\sf\ Area\ of\ square= a^2$

CASE II

Now if the side is increased by 50%

then new side will be

$:\implies\sf\ 50\%\ of\ a\\ \\ \\ :\implies\sf\ \dfrac{50}{100}\times a\\ \\ \\ :\implies\sf\ \dfrac{a}{2}\\ \\ \\ \it\ New\ side\ \\ \\ \\ :\implies\sf\ a+\dfrac{a}{2}\\ \\ \\ :\implies\sf\ New\ side= a+ \dfrac{a}{2}\\ \\ \\ :\implies\sf\ New\ side= \dfrac{3a}{2}$

Now area of square

$:\implies\sf\ Area= \bigg(\dfrac{3a}{2}\bigg)^2\\ \\ \\ :\implies\sf\ Area= \dfrac{9a^2}{4}$

Now the ratio of their Areas

$:\implies\sf\ Ratio= \dfrac{New\ Area}{Original\ Area}\\ \\ \\ :\implies\sf\ Ratio= \dfrac{9a^2/_{4}}{a^2}\\ \\ \\ :\implies\sf\ Ratio= \dfrac{9\cancel{a^2}}{4\cancel{a^2}}\\ \\ \\:\implies\sf\ Ratio= \dfrac{9}{4}\\ \\ \\ \therefore{\purple{\sf\ Ratio\ of\ their\ Areas= 9:4}}$

Option (a) is the correct answer

Answer 2

${\large{\pmb{\sf{\underline{Correct \; question}}}}}$

★ If each side of square is increased by 50 percentage. Then what will be ratio of area of new square to that of area of original square.

(1) 9:4 (2) 5:4 (3) 4:5 (4) 4:9

${\large{\pmb{\sf{\underline{Given \; that}}}}}$

★ Each side of square is increased by 50 percentage.

${\large{\pmb{\sf{\underline{To \; find}}}}}$

★ Ratio of area of new square to that of area of original square.

${\large{\pmb{\sf{\underline{Options \; for \; help}}}}}$

★ 9:4

★ 5:4

★ 4:5

★ 4:9

${\large{\pmb{\sf{\underline{Solution}}}}}$

★ Ratio of area of new square to that of area of original square = 9:4 ; option (1)

${\large{\pmb{\sf{\underline{Full \; Solution}}}}}$

~ As it's given that side of square is increased by 50 percentage. So we don't now too that what is the side of the square. So let's assume that,

↝ Side of the square be x

~ We know that the formula to find area of a square is (given below),

↝ Area of square = Side × Side or (Side)²

~ Now according to the above data,

↝ Area of square = (x)²

~ Now as it's given that side of square is increased by 50 percentage. Henceforth,

↝ Side is increased by 50%

↝ 50% of x

↝ 50% × x

↝ 50/100 × x

↝ 5/10 × x

↝ 1/2 × x

↝ x/2

~ Henceforth, the new side be,

↝ x + x/2

• Now by taking LCM and let's solve

↝ x/1 + x/2

↝ (2×a) + (1×a) /2

↝ 2a + 1a /2

↝ 3a/2

~ Now according to the above information the area of the square be,

↝ Area of square = (3a/2)²

↝ Area of square = 3a/2 × 3a/2

↝ Area of square = 9a²/4

~ Now ratio of their area be,

↝ Ratio of area = New area/Original area

↝ Ratio of area = (9a²/4) / a²

↝ Ratio of area = 9/4

↝ Ratio of area = 9:4

• Henceforth, 9:4 , Option (1) is ratio of area of new square to that of area of original square.