Question

I dont know this. pls help

Answer 1

28, 4 or 4, 28 (order doesn't matter, both are true answers)

Explanation:

l + w = 32

l*w = 112

l = 112/w

112/w + w = 32

w = 28 or 4

l = 28 or 4

Answer 2

4,28

Explanation:

So let's look at the sentence to take any necessary information out. It says the length of a rectangle plus it's width is 32. Since we do not know what the length and width are, let's just represent them as L (length) and W (width). Using this information we get the equation:
`L + W = 32` and since we're given the area of the rectangle, we can also define another equation which is:
`LW = 112` since the length * width = area.

So now all we have is a systems of equations. We can solve for L or W in the area equation and plug it into the addition equation. We can also solve for L or W in the addition equation and then plug it into the area equation, either should work, but in this example I'll solve for L in the addition equation:

Original Equation:

`L + W = 32`

Subtract 32 from both sides

`L = 32-W`

Now let's use this definition of L to plug into the second equation:

`LW = 112 \implies (32-W)W = 112`

Distribute the W

`-W^2+32W=112`

Now if you notice, we simply have a quadratic equation and we can subtract 112 from both sides and then use the quadratic formula:
`x=(-b\pm√(b^2-4ac))/(2a)`

Subtract 112 from both sides

`-W^2+32W-112=0`

Use quadratic formula

`W = (-32\pm√(32^2-4(-1)(-112)))/(2(-1))`

Simplify stuff in radical

`W = (-32\pm√(576))/(-2)`

Calculate the square root

`W=(-32\pm24)/(-2)`

Use positive sign:

`W=(-32+24)/(-2)`

Simplify numerator

`W = (-8)/(-2)`

Simplify fraction

`W=4`

Take negative sign

`W = (-32-24)/(-2)`

Simplify numerator

`W=(-56)/(-2)`

W =
`28`

So we have two solutions, and the reason for this is because had we solved for W in the original equation and substituted that into here, there would be no different, it's not bound by some variable name. So these are actually the two sides of the rectangles

4 + 28 = 32

4 * 28 = 112

4, 28