Question

find sides of square​

Answer 1

Step-by-step explanation:

Step-by-step explanation:

let first = x

second = y

difference in perimeter = 16m

so...

4x - 4y = 16

4(x-y) = 16

x-y = 16/4 = 4

so.... x - y = 4 (where x and y are sides)

x = 4+y

now.. sum of their area =400

x²+y² = 400

putting value of x in this eq..

(4+y)² + y² = 400

( 4²+y²+2*4*y) +y² = 400 (using Identity (a+b)²)

16 +y² +8y +y² = 400

16 +2y² +8y -400 = 0

taking 2 common

2(8+y²+4y-200) = 0

y²+4y - 192 = 0/2

By middle term spillting

y² +16y-12y -192 = 0

y(y+16)- 12(y+16)

(y+16)(y-12) =0

taking first factor = y = -16

taking second factor = y =12

so y = 12 (because in first it is -16 and the side never be negative)

now.. we know that

x-y = 4 (proved above)

x - 12 = 4

x = 4+12 = 16

X=16 and y=12

Answer 2

Question:

The sum of the areas of two squares is 400 sq.m. If the difference between their perimeters is 16 m, find the sides of two squares.

Answer:

Side of first square = 16 m

Side of second square = 12 m

Step-by-step explanation:

Let the sides of the two squares be x m and y m respectively.

Now,

Area of first square = (Side)²

= (x)² m²

= x² m²

Area of second square = (Side)²

= (y)² m²

= y² m²

Perimeter of first square = 4(side)

= 4x m

Perimeter of second square = 4(side)

= 4y m

A.T.Q.

Area of first square + Area of second square = 400 m²

→ x² + y² = 400 ...(i)

Also,

Difference between the perimeters of both squares = 16 m

→ 4x - 4y = 16

→ 4(x - y) = 16

→ x - y = 16/4

→ x - y = 4 ...(ii)

From (ii), we get

→ x = 4 + y ...(iii)

Putting this value in (i), we get

→ (4 + y)² + y² = 400

Identity : (a + b)² = a² + b² + 2ab

Here, a = 4, b = y

→ (4)² + (y)² + 2(4)(y) + y² = 400

→ 16 + y² + 8y + y² = 400

→ 2y² + 8y + 16 = 400

→ 2y² + 8y + 16 - 400 = 0

→ 2y² + 8y - 384 = 0

→ 2(y² + 4y - 192) = 0

→ y² + 4y - 192 = 0

Using Middle Term Factorisation, we get

→ y² - 12y + 16y - 192 = 0

Taking common terms out, we get

→ y(y - 12) + 16(y - 12) = 0

→ (y - 12)(y + 16)

Using zero product rule.

→ (y - 12) = 0 and (y + 16) = 0

→ y = 12 and y = - 16

Side cannot be negative. Hence, y = 12 m

Putting this value in (iii), we get

→ x = 4 + 12

→ x = 16

Hence,

Side of first square = 16 m

Side of second square = 12 m