Question

directions: solve for x.
3.
4.
5.
6.

Explanation:

Problem 3

Step1: Calculate triangle area

$\text{Area} = \frac{1}{2} \times 6 \times 8 = 24$

Step2: Equate area to hypotenuse formula

$24 = \frac{1}{2} \times 10 \times x$

Step3: Solve for $x$

$x = \frac{24 \times 2}{10} = 4.8$

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Problem 4

Step1: Calculate triangle area

$\text{Area} = \frac{1}{2} \times 20 \times 21 = 210$

Step2: Equate area to base formula

$210 = \frac{1}{2} \times 29 \times x$

Step3: Solve for $x$

$x = \frac{210 \times 2}{29} = \frac{420}{29} \approx 14.48$

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Problem 5

Step1: Calculate triangle area

$\text{Area} = \frac{1}{2} \times 48 \times 20 = 480$

Step2: Equate area to hypotenuse formula

$480 = \frac{1}{2} \times 52 \times x$

Step3: Solve for $x$

$x = \frac{480 \times 2}{52} = \frac{240}{13} \approx 18.46$

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Problem 6

Step1: Calculate triangle area

$\text{Area} = \frac{1}{2} \times 13.2 \times 22.4 = 147.84$

Step2: Equate area to hypotenuse formula

$147.84 = \frac{1}{2} \times 26 \times x$

Step3: Solve for $x$

$x = \frac{147.84 \times 2}{26} = 11.37$

Answer:

1. $x = 4.8$
2. $x = \frac{420}{29} \approx 14.48$
3. $x = \frac{240}{13} \approx 18.46$
4. $x = 11.37$