1. **Problem statement:** We have an isosceles triangle with two equal sides of length $x$ cm and a base of 5 cm. The area of the triangle is 12 cm². We need to find the perimeter of the triangle, rounded to 3 significant figures. 2. **Formula for the area of a triangle:** $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ 3. **Step 1: Express the height in terms of $x$** Since the triangle is isosceles, the height bisects the base into two segments of length $\frac{5}{2} = 2.5$ cm. Using the Pythagorean theorem on one of the right triangles formed: $$h = \sqrt{x^2 - 2.5^2} = \sqrt{x^2 - 6.25}$$ 4. **Step 2: Use the area to find $x$** Given area = 12 cm², $$12 = \frac{1}{2} \times 5 \times h = \frac{5}{2} h = 2.5h$$ So, $$h = \frac{12}{2.5} = 4.8$$ 5. **Step 3: Solve for $x$** From step 3, $$4.8 = \sqrt{x^2 - 6.25}$$ Square both sides: $$4.8^2 = x^2 - 6.25$$ $$23.04 = x^2 - 6.25$$ $$x^2 = 23.04 + 6.25 = 29.29$$ $$x = \sqrt{29.29} \approx 5.41$$ 6. **Step 4: Calculate the perimeter** Perimeter $P = x + x + 5 = 2x + 5$ $$P = 2(5.41) + 5 = 10.82 + 5 = 15.82$$ Rounded to 3 significant figures: $$\boxed{15.8}$$ **Final answer:** The perimeter of the triangle is 15.8 cm (to 3 significant figures).