Deltoid Area Problem: Solve for X When Area = 16 cm² and Length = 2×Width

Question

Below is a deltoid with a length 2 times its width and an area equal to 16 cm².


Calculate x.

1616162x2x2xxxx

Video Solution

Solution Steps

00:00 Calculate X
00:03 We'll use the formula for calculating the area of a kite
00:09 (diagonal times diagonal) divided by 2
00:13 We'll substitute appropriate values according to the given data and find X
00:24 We'll simplify what we can
00:30 Extract the root
00:42 And this is the solution to the problem

Step-by-Step Solution

Given the problem, we are tasked to find the value of x x for a deltoid where the length is twice the width and the area is given. Let's proceed as follows:

  • Step 1: In this deltoid problem, the diagonals correspond to length 2x 2x and width x x . The formula for the area of a deltoid in terms of its diagonals is A=12×d1×d2 A = \frac{1}{2} \times d_1 \times d_2 .
  • Step 2: Substitute the values. Thus, the area 16=12×(2x)×x 16 = \frac{1}{2} \times (2x) \times x .
  • Step 3: Simplify the equation: 16=12×2x2=x2 16 = \frac{1}{2} \times 2x^2 = x^2 .
  • Step 4: Solve for x x : We find x2=16 x^2 = 16 , so x=16 x = \sqrt{16} .
  • Step 5: Conclude x=4 x = 4 .

Therefore, the solution to the problem is x=4 x = 4 .

Answer

x=4 x=4

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