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10) So here, in the first figure –

We are given a Rectangle and we know formula for perimeter of a rectangle's given

  • Perimeter = 2 (Length + Width)

In case of 2nd figure a tiangle's given whose formula of Perimeter will be

  • Perimeter = Sum of 3 sides

According to the question :-

↠Perimeter of rectangle = Perimeter of triangle

↠ x+3 +x+5+x+4 = 2 (x+4+x-2)

↠ 3x + 12 = 2(2x+2)

↠ 2(2x+2) = 3x + 12

↠ 4x +4 = 3x+12

↠ 4x-3x +4-12 = 0

↠ x -8 =0

↠ x = 8

  • Henceforth, x will be 8 if they have same Perimeter.

Answer:

In Figure 1 :

We know that, It is a rectangle and the formula for finding the perimeter of a rectangle is :

  • Perimeter = 2( Length + Breadth)

In Figure 2 :

We know that, it is a triangle and the formula for finding the perimeter of a triangle is :

  • Perimeter = Sum of the three sides of the triangle.

[tex] \\ \: \: { \underline{ \underline{ \textbf{\textsf{{ According to the Question \::}{}}}}}}[/tex]

  • Perimeter of the given rectangle = Perimeter of the given triangle.

[tex] \\ \sf \implies \: 2(x - 2 + x+4) = (x + 3) + (x + 4) + (x + 5)\: \: \: \: \: \: \: \\ \\ \sf \implies \: 2(2x +2) = x + 3 + x + 4 + x + 5\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \implies \: 4x + 4 = 3x + 12 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \implies \: 4x - 3x = 12 - 4 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \implies \: x = 8 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\[/tex]

  • Hence, The value of x must be 8 so that the figures have the same perimeter.