Expand by multiply outside term with each of the inside terms to get
6p^3-6p
----------------------------------------------------------------
Define x and y:
----------------------------------------------------------------
Let the length be x.
Let the width be y.
----------------------------------------------------------------
Formula:
----------------------------------------------------------------
Perimeter = 2(Length + Width)
----------------------------------------------------------------
Construct equations and solve for x and y:
----------------------------------------------------------------
2x + 2y = 56 ---------------------- (1)
2(x+8) + 4y = 82 -----------------------(2)
----------------------------------------------------------------
From equation 1:
----------------------------------------------------------------
2x + 2y = 56
x + y = 28
x = 28 - y
----------------------------------------------------------------
From equation 2:
----------------------------------------------------------------
2(x+8) + 4y = 82
2x + 16 + 4y = 82
2x + 4y = 66
x + 2y = 33
----------------------------------------------------------------
Substitute x = 28 - y into equation 2:
----------------------------------------------------------------
x + 2y = 33
(28 - y) + 2y = 33
28 - y + 2y = 33
y = 5
----------------------------------------------------------------
Substitute y = 5 into equation 1:
----------------------------------------------------------------
x = 28 - y
x = 28 - 5
x = 23
----------------------------------------------------------------
Find Length and Width
----------------------------------------------------------------
Length = x = 23 m
Width = y = 5m
----------------------------------------------------------------
Answer: Length = 23m and Width = 5m
----------------------------------------------------------------
Answer:5x
Step-by-step explanation:
Answer:
EF = 20 cm
Step-by-step explanation:
Here, we want to find the length of EF
To do this, we use the principle of similar triangles
The similar triangles we are considering here will be ;
FEA and FBD
when two triangles are similar, the ratio of their corresponding sides are equal
Let us calculate DC first
we can use Pythagoras’ theorem here and it is that the square of the hypotenuse equals the sum of the square of the two other sides
Using the triangle EDC
15^2 = 12^2 + DC^2
DC^2 = 225-144
DC^2 = 81
DC = 9
So the entire length of BD is 9 + 12 = 21 cm
Thus, we have it that;
Let EF be x
so DF = 15 + x
Hence;
BD/DF = AE/EF
21/15+x = 12/x
21x = 12(15 + x)
21x = 180 + 12x
21x-12x = 180
9x = 180
x = 180/9
x = 20 cm
EF = 20 cm
