Recall the formula for finding the area of a rectangle:
Area = Length × Width
Recall the formula for finding the perimeter of a rectangle:
Perimeter = 2 ( Length + Width )
Given in your problem:
Area = 40 sq. units
Perimeter = 26 units
Required to solve for:
Length (L) and width (W)
• First, substitute the given to the formula:
Area = Length x Width
40 = L × W ⇒ equation number 1
Perimeter = 2 ( Length + Width )
26 = 2 ( L + W ) ⇒ equation number 2
• Simplifying equation number 2,
13 = L + W
• Rearranging the equation,
L = 13 - W ⇒ equation 3
Substituting equation 3 from equation 1:
( equation 1 ) 40 = (L)(W)
( equation 3 ) L = 13 - W
40 = (13 - W) (W)
40 = 13W - W²
( regrouping ) W² - 13W + 40 = 0
( factoring ) (W - 8) (W - 5) = 0
W - 8 = 0 ; W - 5 = 0
W = 8 ; W = 5
Therefore, there are 2 possible values for the width of the rectangle. It can be 8 units or 5 units.
• Now to solve for the length of the rectangle, substitute the two values of width to equation 3.
(equation 3) L = 13 - W
for W = 8 ⇒ L = 13 - 8
L = 5 units
for W = 5 ⇒ L = 13 - 5
L = 8 units
Answer:
A. 36
Step-by-step explanation:
Because the two angles at the bottom of both the triangles are congruent, the two triangles are similar. Therefore, the corresponding side lengths of the triangles must be proportional to each other
if the area of a triangle is hb/2,
(with h=length of height, b=length of base)
the height of the first triangle is:
25 = 10h/2
50 = 10h
h=5
you can write ratios representing the proportions of the two triangles:
5/x = 10/12 (with x=height of second triangle)
x=6
then find the area of the second triangle with the height (6) and base (12)
(6*12)/2 = 36
Answer:
4
Step-by-step explanation:
Since x = 5, you can substitute 5 into the x value of the expression: 5 + 5 - 6. Then, you add the 5 + 5 to get 10 in which you subtract 6 from. The answer is 4.
Answer:
The distance is 2.33 π
Step-by-step explanation:
First we have to calculate the perimeter of the circle with the following formula:
r = 14in
c = π * 2r
Now we replace the value of r
c = π * 2 * 14
c = π * 28
c = 28π
Now we have to multiply it by 30/360 which is the fraction that represents the arc over the entire circumference
28π * 30/360 = 2 1/3 π = 2.33 π
Answer:
<h3>
</h3>
<h3>7. Cos Z </h3>
=> Cos theta = Base /Hypotenuse
=> Cos Z = 30/50 => 3/5
★ So, Option <u>B) 3/5 </u> is a correct answer.
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<h3>8. Cos X </h3>
=> Cos theta = Base/Hypotenuse
=> Cos X = 12/37
★ So, option <u>D)</u><u> </u><u>1</u><u>2</u><u>/</u><u>3</u><u>7</u> is a correct answer.
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<h3>9. Sin Z</h3>
=> Sin theta = Perpendicular/Hypotenuse.
Sin Z = 16/20 => 4/5
★ So, option <u>C)</u><u> </u><u>4</u><u>/</u><u>5</u> is a correct answer
<h3>_____________________</h3>
<h3>10. Sin Z </h3>
=> Sin theta = Perpendicular/Hypotenuse
Sin Z = 48/50 => 24/25
★ So, option <u>A)</u><u>2</u><u>4</u><u>/</u><u>2</u><u>5</u> is correct answer
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