Sum of areas of two squares is 468

Asked by admin @ 29/08/2021 in Math viewed by 334 People

sum of the areas of two squares is 468 m square if the difference of their perimeter is 24 m find the sides of the two square

Answered by admin @ 29/08/2021

Answer:

→ 18m and 12 m .

Step-by-step explanation:

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

Case 1 .

→ Sum of the areas of two squares is 468 m² .

A/Q,

∵ x² + y² = 468 . ...........(1) .

[ ∵ area of square = side² . ]

Case 2 .

→ The difference of their perimeters is 24 m .

A/Q,

∵ 4x - 4y = 24 .

[ ∵ Perimeter of square = 4 × side . ]

⇒ 4( x - y ) = 24 .

⇒ x - y = 24/4 .

⇒ x - y = 6 .

∴ y = x - 6 ..........(2) .

From equation (1) and (2) , we get

∵ x² + ( x - 6 )² = 468 .

⇒ x² + x² - 12x + 36 = 468 .

⇒ 2x² - 12x + 36 - 468 = 0 .

⇒ 2x² - 12x - 432 = 0 .

⇒ 2( x² - 6x - 216 ) = 0 .

⇒ x² - 6x - 216 = 0 .

⇒ x² - 18x + 12x - 216 = 0 .

⇒ x( x - 18 ) + 12( x - 18 ) = 0 .

⇒ ( x + 12 ) ( x - 18 ) = 0 .

⇒ x + 12 = 0 and x - 18 = 0 .

⇒ x = - 12m [ rejected ] . and x = 18m .

∴ x = 18 m .

Put the value of 'x' in equation (2), we get

∵ y = x - 6 .

⇒ y = 18 - 6 .

∴ y = 12 m .

Hence, sides of two squares are 18m and 12m respectively .

The sum of areas of two squares is 468

Asked by admin @ 20/08/2021 in Math viewed by 297 persons

sum of the areas of two squares is 468 m square if the difference of their perimeter is 24 m find the sides of the two square

Sum of the areas of two squares is 468

Asked by admin @ 11/08/2021 in Math viewed by 288 persons

sum of the areas of two squares is 468 m square if the difference of their perimeter is 24 m find the sides of the two square

Sum of the areas of two squares is 400

Asked by admin @ 17/08/2021 in Math viewed by 311 persons

sum of areas of two squares is 400 cm 2 .If the difference in their perimeters is 16cm. find the sides of the two squares

The sum of two odd number is always

Asked by admin @ 31/08/2021 in Math viewed by 342 persons

The sum of two odd numbers is always an ____number

The sum of two irrational numbers is always

Asked by admin @ 31/08/2021 in Math viewed by 357 persons

Is the sum of two irrational numbers always irrational? justify your answer.

The two opposite vertices of a square are

Asked by admin @ 31/08/2021 in Math viewed by 329 persons

The two opposite vertices of a square are(-1,2)qnd(3,2) find the coordinate of other two vertices

Sum of two prime numbers is always even

Asked by admin @ 29/08/2021 in Math viewed by 352 persons

Sum of two prime numbers is always even

The sum of two digit number is 9

Asked by admin @ 26/08/2021 in Math viewed by 338 persons

The sum of digits of a two-digit number is 9.Also,nine times this number is twice the number obtained by reversing the order of the digits.Find the number.

If the magnitude of sum of two vectors

Asked by admin @ 26/08/2021 in Physics viewed by 315 persons

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors the angle between these vector is a) 90 b) 45 c) …

The sum of two irrational number is always

Asked by admin @ 25/08/2021 in Math viewed by 300 persons

Is the sum of two irrational numbers always irrational? justify your answer.

The sum of two numbers is 1000

Asked by admin @ 24/08/2021 in Math viewed by 320 persons

The sum of two numbers is 1000 and the difference between their squares is 25600 then find the numbers

Sum of squares of n natural numbers formula

Asked by admin @ 24/08/2021 in Math viewed by 349 persons

Sum of squares of first square of n natural numbers formula

Find two consecutive positive integers whose sum is 76

Asked by admin @ 23/08/2021 in Math viewed by 332 persons

Find two consecutive positive odd integer whose sum is 76

The sum of the digits of a two digit

Asked by admin @ 23/08/2021 in Math viewed by 302 persons

The sum of digits of a two-digit number is 9.Also,nine times this number is twice the number obtained by reversing the order of the digits.Find the number.