Questions: Quadrilateral J K L M is a kite with an area of 63 square feet. What is the length of NM? A 6 ft B 9 ft C 5 ft D 7 ft

Transcript text: Quadrilateral $J K L M$ is a kite with an area of 63 square feet. What is the length of NM? A 6 ft B 9 ft C 5 ft D 7 ft

Solution

Solution Steps

Step 1: Understand the Problem

The problem states that quadrilateral JKLM is a kite with an area of 63 square feet. We need to find the length of NM.

Step 2: Recall the Area Formula for a Kite

The area $ A $ of a kite can be calculated using the formula: \[ A = \frac{1}{2} \times d_1 \times d_2 \] where $ d_1 $ and $ d_2 $ are the lengths of the diagonals.

Step 3: Identify the Diagonals

From the diagram:

One diagonal $ JL $ is given as $ 7 + 7 = 14 $ feet.
The other diagonal $ KM $ is split into two parts: $ KN = 3 $ feet and $ NM $ (which we need to find).

Step 4: Set Up the Equation

Using the area formula: \[ 63 = \frac{1}{2} \times 14 \times (3 + NM) \]

Step 5: Solve for NM

First, simplify the equation: \[ 63 = 7 \times (3 + NM) \] \[ 63 = 21 + 7 \times NM \] Subtract 21 from both sides: \[ 42 = 7 \times NM \] Divide by 7: \[ NM = 6 \]

Final Answer

The length of NM is $ \boxed{6 \text{ ft}} $.

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