Next, increase the base to 12 cm and find the new height \( h' \) using the same method:
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- h = \sqrt{13^2 - 5^2} = \sqrt{169 - 25} = \sqrt{144} = 12 \text{ cm}
- The area of the original triangle is:
- A_1 = \frac{1}{2} \times 10 \times 12 = 60 \text{ cm}^2
- h' = \sqrt{13^2 - \left(\frac{12}{2}\right)^2} = \sqrt{169 - 36} = \sqrt{133}
- The area of the new triangle is:
- A_2 = \frac{1}{2} \times 12 \times \sqrt{133} = 6\sqrt{133} \text{ cm}^2
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