Answer:
b = 40 and -40
General form of Perfect square trinomial is
a
2
+
2
a
b
+
b
2
Therefore from
16
x
2
−
b
x
+
25
a
2
=
√
16
x
2
,
b
2
=
25
, then
a
=
±
4
x
,
b
=
±
5
take consideration a=4x and b=-5 (different sign), then
−
b
x
=
2
(
4
x
)
(
−
5
)
−
b
x
=
−
40
x
b
=
40
The perfect square is
(
4
x
−
5
)
2
=
16
x
2
−
40
x
+
25
.
if we consider a=4x and b=5 (same sign), then
−
b
x
=
2
(
4
x
)
(
5
)
−
b
x
=
40
x
b
=
−
40
The perfect square is
(
4
x
+
5
)
2
=
16
x
2
+
40
x
+
25
.
The first solution
(
4
x
−
5
)
2
is the best solution after comparing the expression given.
Answer:
The area of the rectangle = 50 cm^2.
Step-by-step explanation:
Let the shortest side of the rectangle be x cm.
Perimeter of the rectangle is:
2x + 2(x + 5).
Perimeter of the triangle = 3 * 2x.
As they have the same perimeter:
2x + 2(x + 5) = 3*2x
2x + 2x + 10 = 6x
6x - 2x - 2x = 10
2x = 10
x = 5 cm.
So the area of the rectangle = x(x + 5)
= 5 * 10
= 50 cm^2.
Hi! I'm happy to help!
To solve this, we first need to look at the perimeter equation:
P=2L+2W
We don't know our length, so we can represent it with x. Since our width is 2 feet shorter than x, we can represent it with x-2. Now, we plug these values into our equation:
56=2x+(2(x-2))
Let's simplify what the width is by multiplying:
56=2x+2x-4
Now, let's combine our 2xs
56=4x-4
Now, we just need to solve for x in order to find our length and width.
First, we need to isolate x on one side of the equation. We can do this by adding 4 to both sides:
56=4x-4
+4 +4
60=4x
Now, all we have to do is divide both sides by 4 and x will be fully isolated:
60=4x
÷4 ÷4
15=x
Now that we know x, let's plug this into our previous equations:
L=x=15
<u>L=15</u>
W=x-2=15-2=13
<u>W=13</u>
To verify our answers, we can plug this into our perimeter equation:
56=2(15)+2(13)
56=30+36
56=56
After double checking our answers, we know that our length is 15 and our width is 13.
I hope this was helpful, keep learning! :D
Hey there! How is your day going?
Sorry if I'm a bit rusty here, math isn't my best subject, necessarily.
If you will notice ABCD is similar in size to EFGH, but the measurements are multiplied by 5. So, all we need to do is multiply the area of ABCD by 5.
35 x 5 = 175
So, your answer is 175 ft²
I hope this helped you, as it has helped me learn a different way to find the area of a rectangle. And I hope you have a very nice day!
Your friend in answering and in need,
~Steve