Math, asked by ali1312hashim, 1 month ago

A wire of length 200 cm is cut into two parts and each part is bent to form a square. If the sum of the areas of the two squares is 425 cm^2, Find the lengths of the sides of the two square​

Answers

Answered by mathdude500
3

\large\underline{\sf{Solution-}}

Let

  • The length of first part be 4x cm

and

  • The other part be 4y cm.

Since, total length = 200 cm

So

\rm :\longmapsto\:4x + 4y = 200

\rm :\longmapsto\:x + y = 50 -  - (1)

Now,

first part of length 4x cm is converted in to square,

So,

  • Perimeter of square = 4x

This implies,

  • The side of first square = x cm

So,

  • Area of square = x²

Also,

Second part of length of 4y cm is converted in to square.

This implies,

  • The side of square = y cm.

So,

  • Area of square = y²

Now,

It is given that

Sum of the area of squares = 425

\rm :\longmapsto\: {x}^{2}  +  {y}^{2} = 425

\rm :\longmapsto\: {x}^{2}  +  {(50 - x)}^{2} = 425  \:  \:  \:  \:  \:  \{ \: using \: (1)  \:  \: \}

\rm :\longmapsto\: {x}^{2} + 2500 +  {x}^{2} - 100x = 425

\rm :\longmapsto\: 2{x}^{2} - 100x + 2075 =  0

So,

Using quadratic formula,

\rm :\longmapsto\:x = \dfrac{100 \: \pm \:  \sqrt{ {(100)}^{2}- 4(2)(2075)}}{2 \times 2}

\rm :\longmapsto\:x = \dfrac{100 \: \pm \:  \sqrt{ 10000- 16600}}{4}

\rm :\longmapsto\:x = \dfrac{100 \: \pm \:  \sqrt{ ( - 6600)}}{4}   \cancel\in \: real \: number

Hence, no such square is possible.

Additional Information :-

Writing Systems of equations from Word Problem.

1. Understand the problem.

  • Understand all the words used in stating the problem.

  • Understand what you are asked to find.

2. Translate the problem to an equation.

  • Assign a variable (or variables) to represent the unknown.

  • Clearly state what the variable represents.

3. Carry out the plan and solve the problem.

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