Mathematics, 21.10.2019 13:20 ceejay8005

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.

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Answer from: qveenriles3714

longer side: 24 inshorter side: 10 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.

Answer from: withrowrj

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:

P = 2(l + h)

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

$l^{2} + h^{2} = d^{2}$

In this problem, we have that:

P = 68, d = 26

$l^{2} + h^{2} = 26^{2}$

$l^{2} + h^{2} = 676$

$h^{2} = 676 - l^{2}$

$h = \sqrt{676 - l^{2}}$

-------

P = 2(l + h)

P = 2l + 2h

$P = 2l + 2\sqrt{676-l^{2}}$

$68 - 2l = 2\sqrt{676 - l^{2}}$

$(68 - 2l)^{2} = (2\sqrt{676 - l^{2}})^{2}$

$4l^{2} - 272l + 4624 = 4(676 - l^{2})$

$4l^{2} - 272l + 4624 = 2704 - 4l^{2}$

$8l^{2} - 272l + 1920 = 0$

The roots are l = 24 and l = 10.

For the height, we have that:

$h = \sqrt{676 - l^{2}}$

When l = 10

$h = \sqrt{676 - l^{2}} = \sqrt{676 - l^{2}} = \sqrt{576} = 24$

When l = 24

$h = \sqrt{676 - l^{2}} = \sqrt{676 - l^{2}} = \sqrt{100} = 10$

Longer side is 24 in

Shorter side is 10 in.

Answer from: Quest

whats the

Answer from: Quest

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = $\frac{-8+3}{4-7}$ = - $\frac{5}{3}$

y = - $\frac{5}{3}$ x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - $\frac{20}{3}$ + c ⇒ c = - $\frac{4}{3}$

y = - $\frac{5}{3}$ x - $\frac{4}{3}$ ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form

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