Question

the perimeter of a quadrilateral (four - sided polygon) is 53 inches. the longest side is four times as long as the shortest side. the other two sides are equally long and are 2 inches longer than the shortest side. find the length of all four sides. the length of the shortest side is □ the length of each of the two equal sides is □ and the length of the longest side is □

Explanation:

Step1: Let the length of the shortest side

Let the length of the shortest side be \(x\) inches. Then the length of the longest side is \(4x\) inches, and the length of each of the other two equal - sided is \((x + 2)\) inches.

Step2: Use the perimeter formula

The perimeter of a quadrilateral is the sum of the lengths of its four sides. So, \(P=x+(x + 2)+(x + 2)+4x\). Given that \(P = 53\) inches.

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Step3: Solve for \(x\)

Subtract 4 from both sides of the equation \(7x+4 = 53\): \(7x=53 - 4=49\). Then divide both sides by 7: \(x=\frac{49}{7}=7\).

Step4: Find the lengths of other sides

The length of each of the two equal sides: \(x + 2=7+2 = 9\) inches. The length of the longest side: \(4x=4\times7 = 28\) inches.

Answer:

The length of the shortest side is \(7\) inches, the length of each of the two equal sides is \(9\) inches, and the length of the longest side is \(28\) inches.