1. The problem describes four instances of triangles with labeled side lengths and bases, along with rectangles labeled with time or distance units. 2. We need to analyze the triangles to solve for unknown sides or verify given side lengths using the Pythagorean theorem or proportion as needed. 3. First row left triangle: sides are 75s and 85s, base is 20s. Check if 75s, 85s, and 20s satisfy Pythagorean theorem $$a^2 + b^2 = c^2$$. - Let's consider 85s as the hypotenuse, so $$75^2 + 20^2 = 5625 + 400 = 6025$$ and $$85^2 = 7225$$. - Since 6025 \neq 7225, the sides do not form a right triangle; the labeling might indicate different meaning or need clarification. 4. First row right triangle: sides are 84cm, 32cm, and base 84cm. - Sides 84cm, 32cm, and 84cm suggest isosceles triangle with two equal sides 84cm. - To verify if it is right triangle: check if $$32^2 + 84^2 = 84^2$$? - $$32^2 + 84^2 = 1024 + 7056 = 8080$$ and $$84^2 = 7056$$, so no right triangle. 5. Second row left triangle: sides 134cm, 56cm, unknown base, rectangle labeled 3m. - Use Pythagorean theorem to find base: $$\text{base} = \sqrt{134^2 - 56^2} = \sqrt{17956 - 3136} = \sqrt{14820} \approx 121.77cm$$. 6. Second row right triangle: sides 200cm, 150cm, and base 100cm, rectangle labeled m. - Check if it fits Pythagorean theorem: $$150^2 + 100^2 = 22500 + 10000 = 32500$$ and $$200^2 = 40000$$. - Since 32500 \neq 40000, no right triangle relationship. 7. Summary: The only unknown base is in the second row left triangle, calculated about 121.77cm.