Question

The area of a rectangle is 490in^2. The ration of the length to the width is 5:2. Find the length and the width

Answer 1

Question #25350

The area of a rectangle is 490in^2. The ration of the length to the width is 5:2. Find the length and the width.

Solution: Suppose that the value of the length will be - $x$, and the value of width - $y$. We can construct the following system of linear equations with two unknowns:

$$\left\{ \begin{array}{l} x \times y = 490 \\ \frac{x}{y} = \frac{5}{2} \end{array} \right. \quad \rightarrow \quad \left\{ \begin{array}{l} x \times y = 490 \\ x = \frac{5y}{2} \end{array} \right.$$

Substitute the value of $x$ into the first equation:

$$\frac{5y}{2} \times y = 490 \quad \rightarrow \quad \frac{5y^2}{2} = 490 \quad \rightarrow \quad 5y^2 = 980 \quad \rightarrow \quad y^2 = 196 \quad \rightarrow \quad y = \pm 14.$$

Since the width of the negative is not for us, which we recline and leave only positive. So $y = 14$.

$$x = \frac{5 \times 14}{2} = \frac{70}{2} = 35.$$

Answer: length - 35, width - 14.