Question

rectangle has a perimeter of 968 ft, then length is 152 more than the width. find the width

Answer 1

QUESTION:

rectangle has a perimeter of 968 ft, then length is 152 more than the width. find the width

SOLUTION:

Let's denote the length of rectangle as $\mathbf{a}$ , and the width of rectangle as $\mathbf{b}$

Hence, the perimeter of rectangle

$$a + a + b + b = 2a + 2b = 968 \text{ ft}$$

And

$$a - b = 152$$

Hence

$$\left\{ \begin{array}{l} 2a + 2b = 968 \\ a - b = 152 \end{array} \right. \Rightarrow \left\{ \begin{array}{l} a + b = \frac{968}{2} \\ a - b = 152 \end{array} \right. \Rightarrow \left\{ \begin{array}{l} a + b = 484 \\ a - b = 152 \end{array} \right. \Rightarrow$$ $$\Rightarrow \left\{ \begin{array}{l} a + b = 484 \\ a = 152 + b \end{array} \right. \Rightarrow \left\{ \begin{array}{l} 152 + b + b = 484 \\ a = 152 + b \end{array} \right. \Rightarrow \left\{ \begin{array}{l} 2b = 484 - 152 \\ a = 152 + b \end{array} \right. \Rightarrow$$ $$\Rightarrow \left\{ \begin{array}{c} b = 166 \\ a = 152 + 166 \end{array} \right. \Rightarrow \left\{ \begin{array}{c} b = 166 \\ a = 318 \end{array} \right.$$

ANSWER:

the length of rectangle is 318 ft, the height of rectangle is 166 ft