The first step to solve this problem is to find the area of
the rectangular piece of fabric.
A of triangle = bh/2
A = (14 cm) (6 cm) /2
A = 84 cm^2 / 2
A = 42 cm
And since there are 31 pieces of the fabric, the total area
of all the pieces of fabric is:
31 pieces of fabric x 42 square centimeters per piece =
1,302 square centimeters
To computer how many congruent triangular patches can be
cut, you have to divide the total area of the fabric pieces with the area of
the congruent triangle:
1,302 square centimeters / 21 square centimeters = 62
Therefore, Leia can cut 62 patches.
Answer:
x = √30
Step-by-step explanation:
From small triangle BDC:
using Pythagorean theorem
CB² = BD² + DC²
x² = BD² + 3²
Fron triangles BDC and ADB.
ΔBDC has long leg BD and short leg DC.
ΔADB has long leg AD and shirt leg BD.
AD : BD = BD : DC
7 : BD = BD : 3
7*3 = BD*BD
BD² = 7*3 = 21
x² = BD² + 3² = 21+9 = 30
x² = 30
x = √30
Notice that
(1 + <em>x</em>)(1 + <em>y</em>) = 1 + <em>x</em> + <em>y</em> + <em>x y</em>
So we can add 1 to both sides of both equations, and we use the property above to get
<em>a</em> + <em>b</em> + <em>a b</em> = 76 ==> (1 + <em>a</em>)(1 + <em>b</em>) = 77
and
<em>c</em> + <em>d</em> + <em>c d</em> = 54 ==> (1 + <em>c</em>)(1 + <em>d</em>) = 55
Now, 77 = 7*11 and 55 = 5*11, so we get
<em>a</em> + 1 = 7 ==> <em>a</em> = 6
<em>b</em> + 1 = 11 ==> <em>b</em> = 10
(or the other way around, since the given relations are symmetric)
and
<em>c</em> + 1 = 5 ==> <em>c</em> = 4
<em>d</em> + 1 = 11 ==> <em>d</em> = 10
Now substitute these values into the desired quantity:
(<em>a</em> + <em>b</em> + <em>c</em> + <em>d</em>) <em>a</em> <em>b</em> <em>c</em> <em>d</em> = 72,000
Answer:
12(2r + 3) is the completed form.
