Sum of the Areas of two Squares is `468m^2`. If the Differences of their Perimeters is 24 m, Find the Sides of Two Squres | Bzziii.com

By admin -
Sum of the areas of two squares is `468m^2`. If the differences of their perimeters is 24 m, find the sides of two squres.

Divide the polynomial p(`x`) by the polynomial g(`x`), and the find the quotient and the remainder.

p(`x`)=`x^4-5x+6,` `g(x)= 2-x^2`







Let side of square 1 be x metres
Perimeter of square 1 = 4`\times`Side = 4x

Now, it is given that
Differences of Perimeter of square is 24 m
Perimeter of square 1 - Perimeter of square 2 = 24

4x - Perimeter of square 2
4x - 24 = Perimeter of square 2
Perimeter of square 2 = 4x - 24 

Now, 
Perimeter of square 2 = 4x - 24 
4`\times`(Side of square 2) = 4x - 24

Side of square 2 = `"4x-25"/"4"` = `"4(x-6)"/"4"` = x-6

Hence, 
Side of square 1 is x
& Side of square 2 is x-6

Also, given that
Sum of area of square is 468`"m"^2`
Area of square 1 + Area of square 2 = 468
`"(Side of square 1)"^2` + `"(Side of square 1)"^2` = 468
`x^2 + (x - 6)^`= 468
`x^2` + `x^2` - 2 `\times` `x` `\times`6 + `6^2` = 468
`x^2` + `x^2` - 12 `x` + 36 = 468
`x^2` + `x^2` - 12 `x` + 36 - 468 = 0
2`x^2` - 12 `x` - 432 = 0


Dividing both sides by 2 `\frac{2x^{2}-12x-432}{2}`= `0/2`
`x^2` - 6`x` - 216 = 0

Comparing equation with a`x^2`+ bx +c = 0,

Here, a = 1, b = -6, c = -216

We Know that, 

D = `b^2` - 4ac

D = `(-6)^2` - 4 `\times` 1 `\times`(-216)

D = 36 + 4 `\times` 216

D = 36 + 864

D = 900

So, the roots to equation are 

x = `\frac{-b\pm\sqrt{D}}{2a}`

Now, Putting Values

x = `\frac{-(-6)\pm\sqrt{900}}{2\times1}`

x = `\frac{6\pm\sqrt{900}}{2\times1}`

x = `\frac{6\pm\sqrt{900}}{2}`

x = `\frac{6\pm\sqrt{9 \times 100}}{2}`

x = `\frac{6\pm\sqrt{3^2 \times 10^2}}{2}`

x = `\frac{-(-6)\pm\sqrt{3^2}\sqrt{10^2}}{2}`

x = `\frac{6\pm3\times10}{2}`

x = `\frac{6\pm30}{2}`


Now, Solving them,


`x` = `"6 + 30"/"2"`

`x` = `36/2`

`x` = 18
 `x` = `"6 - 30"/"2"`

`x` = `-24/2`

`x` = -12

So, `x` = 18 &  `x` = -12

Since `x` is side of square and `x` cannot be negative 
So, x = 18 is the solution

∴ Side of Square 1 = `x` = 18 m
& Side of square 2 = `x` - 6 = 18 - 6 = 12 m

Comments

Post a Comment

Popular posts from this blog

Explain the Role of ‘Justice Party’ in Boycotting of Council Elections | bzziii.com

By admin -
answer source Question Read the source given below and answer the questions that follows: Source : The Movement in the Towns The movement started with middle-class participation in the cities. Thousands of students left government-controlled schools and colleges, headmasters and teachers resigned, and lawyers gave up their legal practices. The council elections were boycotted in most provinces except Madras, where the Justice Party, the party of the non-Brahmans, felt that entering the council was one way of gaining some power–something that usually only Brahmans had access to. The effects of non-cooperation on the economic front were more dramatic. Foreign goods were boycotted, liquor shops picketed, and foreign cloth burnt in huge bonfires. The import of foreign cloth halved between 1921 and 1922, its value dropping from Rs. 102 crore to Rs. 57 crore. In many places merchants and traders refused to trade in foreign goods or finance foreign trade. As the boycott movement spread...
Read more

Who do you think is the ‘well-dressed customer’ at the shop?

By admin -
Read the following passage. At the shop there was a well-dressed customer. He bent down and asked the little girl, “What kind of a miracle does your brother need? “I don’t know,” she replied with her eyes welling up. “He’s really sick and Mummy says he needs an operation. But my Daddy can’t pay for it, so I have brought my savings.” “How much do you have?” asked the man. “One dollar and eleven cents, but I can try and get some more,” she answered barely audible. Answer the following questions. 1) Who do you think is the ‘well-dressed customer’ at the shop? 2) What did the well-dressed man ask the little girl? 3) “He’s really sick.” Who does title word ‘he’ refer to here ? What is he to Tess? 4) What did he need urgently? 5) How much money did the little girl have with her? SOLUTION 1. I think the well-dressed customer at the shop is Dr. Carlton Armstrong. 2. The well-dressed man asked the little girl what kind of a miracle her brother needed. 3. The word ‘he’ refers to A...
Read more

Fraction becomes 9/11, If 2 is Added to Both the Numerator and Denominator. If 3 is Added to Both the Numerator and the Denominator, it Becomes 5/6. Find the Fraction. | Bzziii.com

By admin -
A fraction becomes `9/11`, if 2 is added to both the numerator and denominator. If 3 is added to both the numerator and the denominator, it becomes `5/6`. Find the fraction. SOLUTION Let Numerator be x & Denominator be y So, Fraction is = `x/y` Given that, If 2 is added to both the numerators and denominator, fraction becomes `9/11` `"Numerators + 2"/"Denominator + 2"`= `9/11` `"x+ 2"/"y + 2"`= `9/11` 11 (`x + 2`) = 9 (`y + 2`) 11`x` + 22 = 9`y` + 18 11`x` - 9`y` = 11 - 22 11`x` - 9`y` = -4 .......(1) Also, Given that if 3 is added to both the numerator and the denominator, fraction become `5/6` `"Numerators + 3"/"Denominator + 3"`= `5/6` `"x+ 3"/"y + 3"`= `5/6` 6 (`x + 3`) = 5 (`y + 3`) 6`x` + 18 = 5`y` + 15 6`x` - 5`y` = 15 - 18 6`x` - 5`y` = - 3 .......(2) Hence, our equations are 11`x` - 9`y` = -4 .......(1) 6`x` - 5`y` = - 3 .......(2) From equation (1...
Read more