Formula for perimeter of a rectangle = 2(L + W)
let the number be x
width = 2x + 8
length = 3(2x + 8)
substitute respectively
96 = 2 (2x + 8 + 3(2x + 8)) open the bracket
96 = 2 ( 2x + 8 + 6x + 24) collect like terms
96 = 2 (8x + 32) open the bracket
96 = 16x + 64
collect like terms
96 - 64 = 16x
32 = 16x
divide both sides by 16
32/16 = 16x/16
2 = x
therefore, the width = 2x + 8 = 2(2) + 8 = 4 + 8 = 12.
and the length = 3(2x + 8) = 6x + 24 = 6(2) + 24 = 12 + 24 = 36.

4 0

3 years ago

Find the value of k so that 48x-ky=11 and (k+2)x+16y=-19 are perpendicular lines.

Rufina [12.5K]

Answer: k = -1 +/- √769

Step-by-step explanation:

48x - ky = 11

-48x -48x

-ky = -48x + 11

$\frac{-ky}{-k} = \frac{-48x}{-k} + \frac{11}{-k}$

$y =\frac{48x}{k} - \frac{11}{k}$

Slope: $\frac{48}{k}$

*************************************************************************

(k + 2)x + 16y = -19

- (k + 2)x -(k + 2)x

16y = -(k + 2)x - 19

$\frac{16y}{16} = -\frac{(k + 2)x}{16} - \frac{19}{16}$

$y = -\frac{(k + 2)x}{16} - \frac{19}{16}$

Slope: $-\frac{(k + 2)}{16}$

**********************************************************************************

$\frac{48}{k}$ and $-\frac{(k + 2)}{16}$ are perpendicular so they have opposite signs and are reciprocals of each other. When multiplied by its reciprocal, their product equals -1.

$-\frac{(k + 2)}{16}$ * $\frac{k}{48}$ = -1