How can Jared use a 100 ft rope to complete …

Mathematics Questions

Jared is using a 100 ft rope to set up a kite-shaped area for food vendors. He has started roping off the area as shown below, and has one more stake to place. How can Jared use all of the rope to complete the kite shape? Explain.

Short Answer

A kite is a quadrilateral with two pairs of congruent adjacent sides, while the opposite sides are not equal. Jared used 60 ft of rope for one pair, leaving 40 ft for the second, allowing him to create another pair of sides measuring 20 ft each, making the kite’s sides unequal.

Step-by-Step Solution

Step 1: Understand the Structure of a Kite

A kite is a specific type of quadrilateral that features two pairs of congruent adjacent sides. This means that the sides next to each other are equal in length. Notably, the opposite sides of a kite are not equal, distinguishing it from other quadrilaterals like rectangles or squares.

Step 2: Assess the Rope Usage

Jared has utilized 60 ft of rope to form one pair of congruent adjacent sides of the kite. Since he initially had a total of 100 ft of rope, he now has 40 ft remaining. This remaining length needs to be divided into two equal parts to create another pair of congruent adjacent sides.

Step 3: Calculate the Length for the Second Pair

To achieve the second pair of congruent adjacent sides, Jared needs to allocate the remaining 40 ft of rope equally. He can use 20 ft for each of the new sides. Since he already has sides measuring 30 ft in the first pair, and he is creating a different length for the second pair, the kite will have opposite sides that are not congruent.

Related Concepts

Kite

A quadrilateral with two pairs of congruent adjacent sides, where the opposite sides are not equal in length.

Congruent Adjacent Sides

Two sides of a shape that are equal in length and share a common vertex.

Rope Usage

The amount of rope used to create the sides of the kite, which must be divided to maintain the congruence of adjacent sides.

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