# One side of a rectangle is 6 longer than the adjacent side. The area is 187. What are the dimensions?

May 2, 2018

$17$ and $11$

#### Explanation:

The area of a rectangle is $A = l \cdot w$. We can use variable $x$ for $l$, and since we know the other side is $6$ longer, we can use $\left(x + 6\right)$ for this side. And we know $A = 187$. Inputting these values:
$187 = x \left(x + 6\right)$ Distribute:
$187 = {x}^{2} + 6 x$ Set equal to $0$:
${x}^{2} + 6 x - 187 = 0$ $11 , 17$ are factors of 187 and can be subtracted to $6$, so we can factor the equation:
$\left(x + 17\right) \left(x - 11\right) = 0$
$17$ and $11$ work for the situation, so they are the dimensions.

May 2, 2018

The sides of the rectangle are 11 and 17.

#### Explanation:

let a,b be the sides of the rectangle with b being the loonger side
$b = a + 6$
Thus $a \cdot b$ = area of rectangle
$a \left(a + 6\right) = 187$
${a}^{2} + 6 a = 187$
${a}^{2} + 6 a - 187 = 0$
${a}^{2} + 17 a - 11 a - 187 = 0$
$a \left(a + 17\right) - 11 \left(a + 17\right) = 0$
$\left(a + 17\right) \left(a - 11\right) = 0$
$a = 11$ or $- 17$
a=positve number
$a = 11$
$b = a + 6$
$b = 11 + 6 = 17$

therefore the sides of the rectanlge are 11 and 17.