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The perimeter of a kite is 50 mm. The length of one of its sides is 1 mm more than twice the length of another. Find the length of the LONGEST side of the kite. Only write the value of the longest side.

Answer :

MrRoyal

Answer:

The length of the longest side is 13mm

Step-by-step explanation:

Represent the two sides with a and b, where a is the longest

[tex]Perimeter = 50[/tex]

[tex]a=b + 1[/tex]

Required

Determine the length of the longest side

Perimeter of a kite is calculated as thus:

[tex]Perimeter = 2(a + b)[/tex]

Make b the subject in [tex]a=b + 1[/tex]

[tex]b = a -1[/tex]

Substitute a - 1 for b and 50 for Perimeter in [tex]Perimeter = 2(a + b)[/tex]

[tex]50 = 2(a + a - 1)[/tex]

Divide through by 2

[tex]25 = a + a - 1[/tex]

[tex]25 = 2a- 1[/tex]

Add 1 to both sides

[tex]25 + 1 = 2a - 1 +1[/tex]

[tex]25 + 1 = 2a[/tex]

[tex]26 = 2a[/tex]

Solve for a

[tex]a = 26/2[/tex]

[tex]a = 13[/tex]

Hence, the length of the longest side is 13mm

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