Aframe shop has been commissioned to frame 5 black-and-white photos for an island resort. each photo has a perimeter of 68 in. and a diagonal of 26 in. find the dimensions of the photos.

longer side is __in.
shorter side is __in.

Step-by-step explanation:

The diagonal of 26 only has factors of 2 and 13, so offers a clue to the solution. 5-12-13 is a Pythagorean triple often used in algebra problems. Here, a picture with double those leg/hypotenuse values would have dimensions 10×24 with a diagonal of 26. The 10×24 dimensions will give a half-perimeter of 10+24 = 34, so a perimeter of 68.

The picture dimensions are 24 in long by 10 in wide.

If you don't happen to make the connection between Pythagorean triples and picture dimensions, you can write and solve an equation for the dimensions.

We know the perimeter is 2 times the sum of length and width, so that sum is 34 inches. If w is the width, 34-w is the length. The diagonal is found using the Pythagorean theorem:

  26^2 = w^2 +(34-w)^2 . . . . . . . . . . . . c^2 = a^2 + b^2

  676 = w^2 + 1156 - 68w +w^2 . . . . . eliminate parentheses

  w^2 -34w +240 = 0 . . . . . . subtract 676, divide by 2

  (w -10)(w -24) = 0 . . . . . . . . factor

Solutions to this equation are ...

  w = 10  or  w = 24

One of these is the length; the other is the width.

The longer side is 24 inches; the shorter side is 10 inches.

Longer side is 24 in

Shorter side is 10 in.

Step-by-step explanation:

A rectangular photo has two dimensions, height h and length l. The height and the length are the two sides.

The perimeter of a rectangle is given by the following formula:

The diagonal is the hypothenuse of a rectangular triangle, with the length and height being the sides. So

In this problem, we have that:

So

-------

The roots are l = 24 and l = 10.

For the height, we have that:

When l = 10

When l = 24

So

Longer side is 24 in

Shorter side is 10 in.

  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.