1. **State the problem:** We have a rectangular garden with a square flower bed of side length $x$ meters in one corner. The lawn surrounds the flower bed, and the total lawn area is 50 m². We need to: a) Form an equation in terms of $x$. b) Solve the equation. c) Calculate the length and width of the whole garden. 2. **Form an equation:** Let the length of the garden be $L$ and the width be $W$. The flower bed is a square with side $x$, so its area is $x^2$. The lawn area is the total garden area minus the flower bed area: $$\text{Lawn area} = L \times W - x^2 = 50$$ From the problem, the lawn dimensions are shown as $(L - x)$ by $(W - x)$, so the lawn area can also be expressed as: $$(L - x)(W - x) = 50$$ 3. **Express $L$ and $W$ in terms of $x$:** Assuming the garden dimensions are such that the lawn forms a rectangle around the flower bed, the total garden dimensions are: $$L = x + a$$ $$W = x + b$$ where $a$ and $b$ are the lawn lengths along the length and width respectively. From the lawn area: $$(L - x)(W - x) = ab = 50$$ Since $a$ and $b$ are constants (given by the lawn dimensions), we can write: $$a \times b = 50$$ 4. **Solve the equation:** If the lawn dimensions are given (for example, $a = 5$ and $b = 10$), then: $$5 \times 10 = 50$$ So the garden dimensions are: $$L = x + 5$$ $$W = x + 10$$ 5. **Calculate the length and width of the whole garden:** If the flower bed side length $x$ is known or found by solving the equation, substitute $x$ back to find $L$ and $W$. **Note:** Since the problem does not provide specific lawn dimensions $a$ and $b$, we cannot find numeric values for $x$, $L$, and $W$ without additional information. **Summary:** - Equation: $$(L - x)(W - x) = 50$$ - Solve for $x$ if $L$ and $W$ or lawn dimensions are known. - Calculate $L$ and $W$ using $L = x + a$, $W = x + b$. Since the problem lacks specific lawn dimensions, the solution is expressed in terms of $x$, $L$, and $W$.