Question

the side of two square fields are in the ratio of 4:5 the area of the larger field sides is 1296 m2 greater than the area of the smaller.the area of the largest field is​

Answer 1

Answer:

3600 m²

Step-by-step explanation:

Let the ratio be 4x : 5x.

Area of smaller field = (4x)² = 16x²

Area of larger field = (5x)² = 25x²

According to Question,

25x² - 16x² = 1296

9x² = 1296

x² = 1296 ÷ 9

x² = 144

x = √144

x = 12

Hence, side of larger field = 60m

Area of larger field = (60m)² = 3600 m²

Answer 2

$\Large{\underline{\underline{\mathfrak{\bf{Question}}}}}$

The side of two square fields are in the ratio of 4:5 the area of the larger field sides is 1296 m² greater than the area of the smaller . The area of the largest field is ?

$\Large{\underline{\underline{\mathfrak{\bf{Solution}}}}}$

$\Large{\underline{\mathfrak{\bf{\orange{Given}}}}}$

• The side of two square fields are in the ratio of 4:5
• The area of the larger field sides is 1296 m² greater than the area of the smaller

$\Large{\underline{\mathfrak{\bf{\orange{Find}}}}}$

• The area of the largest field ?

$\Large{\underline{\underline{\mathfrak{\bf{Explanation}}}}}$

Let,

• Side of largest square = x
• Side of smallest square = y

Condition first :-

( The area of the larger field sides is 1296 m² greater than the area of the smaller .)

➠ The area of the larger field sides = The area of the smaller field sides + 1269

➠ x² = y² + 1296

➠ x² - y² = 1296 ..................(1)

Again,

Condition second:-

( The side of two square fields are in the ratio of 4:5 )

➠ y : x = 4 : 5

➠ y/x = 4/5

➠ 4x - 5y = 0 ............(2)

Or,

➠ x = 5y/4 ............(3)

keep value of x in equ(1),

➠ (4y/5)² - y² = 1296

➠ 25y²/16 - y² = 1286

➠ 25y² - 16y² = 1296 × 16

➠ 9y² = 1296 × 16

➠ y² = (1296 × 16)/9

➠ y² = 144 × 16

➠ y = √(144×16)

➠ y = 12×4

➠ y = 48

Keep value of y in equ(2),

➠ 4x - 5 × 48 = 0

➠ 4x = 240

➠ x = 240/4

➠ x = 60

Hence:-

• Side of largest square = 60 m
• Side of smallest square = 48 m

Now,

★ Area of largest square field = (side)²

➠ Area of largest square field = (60)²

➠ Area of largest square field = 3600 m²

$\Large{\underline{\mathfrak{\bf{\orange{Answer\:verification}}}}}$

( The side of two square fields are in the ratio of 4:5 )

➠ (Side of smallest square):(Side of largest square) = 4:5

➠ 48:60 = 4:5

We , can write this in division form

➠ 48/60 = 4/5

Divide by 12

➠ 4/5 = 4/5

Or,

➠ 4 : 5 = 4 : 5

L.H.S. = R.H.S.

That's proved