Answer:
Length = 13 cm.
Step-by-step explanation:
If the length is L and the width is W we have the system:
2L + 2W = 32
LW = 39
From the first equation:
L + W = 16 and
L = 16 - W
Substitute this in the second equation:
W(16 - W) = 39
16W - W^2 = 39
W^2 - 16W + 39 = 0
(w - 13)(W - 3) = 0
W = 13, 3
As W < L, W must be 3 because L = 16-13 = 3 does not make sense.
So Length = 16 - 3 = 13.
1. 75/300 = x/48 (your proportion)
2. x= 12
3. 30/240 = x/24 (your proportion)
4. x= 3
Your answer would come out to 15 miles total.
Longer leg = x + 4
Shorter leg = x
Hypotenuse = x + 8
Using Pythagorean Theorem:
a^2 + b^2 = c^2
(x + 4)^2 + x^2 = (x + 8)^2
x^2 + 8x + 16 + x^2 = x^2 + 16x + 64
2x^2 + 8x + 16 = x^2 + 16x + 64
2x^2 +8x = x^2 + 16x + 48
2x^2 - 8x = x^2 + 48
x^2 - 8x = 48
x^2 - 8x - 48 = 0
You can complete the square from here or use the quadratic formula.
Completing the square:
x^2 - 8x = 48
x^2 - 8x + (-8/2)^2 = 48 + (-8/2)^2
x^2 - 8x + 16 = 48 + 16
(x - 4)(x - 4) = 64 or (x - 4)^2 = 64
x - 4 = +√64 OR x - 4 = -√64
x - 4 = +8 OR x - 4 = -8
x = 12 OR x = -4
However, you can't use negative 4 as a length because your length needs to be a positive.
So x will be 12.
Shorter leg: 12
Longer leg: 12 + 4
Hypotenuse: 12 + 8
The expression that expresses all possible lengths of segment AB is 27 < AB < 81. The correct option is the second option 27 < AB < 81
<h3>Properties of a triangle</h3>
From the question, we are to determine the expression that expresses all possible lengths of segment AB
From one of the properties of a triangle,
The <u>third side</u> of any triangle is greater than the difference of the other <u>two sides</u>; and the <u>third side</u> of any triangle is lesser than the sum of the <u>two other sides</u>
Then, we can write that
AB < 27 + 54
and
AB > 54 - 27
Putting the two inequalities together, we get
54 - 27 < AB < 27 + 54
27 < AB < 81
Hence, the expression that expresses all possible lengths of segment AB is 27 < AB < 81. The correct option is the second option 27 < AB < 81
Learn more on the Properties of a triangle here: brainly.com/question/1851668
#SPJ1
