Let's first say that L=W+44
and then remember that perimeter is P=2L+2W
replace the L with W+44
we then get P=2(W+44)+2W, now I'll solve it
P=2W+88+2W
P=4W+88
substitute 288 for P
288=4W+88
200=4W
50=W
so now we now how wide the court is. add 44 to find the length which gives you L=94
as always plug the numbers back into your perimeter equation to ensure L and W are correct
Answer:
215.20 ft^2
Step-by-step explanation:
The figure has 2 semi-circles.
First we find the area of each circle using the formula 
because that is the area formula for a circle.
The semi-circle to the left gives the diameter which is 22 feet. The radius would be half the diameter thus r=11 for semi-circle one.
Then we are to find the diameter of the second semi-circle. Given the entire length to be 30 feet, 30-22 leaves us with 8 feet as its diameter thus r=4.
Left: r=11
Right: r=4
Then, plugging both into the formula for area of a circle, we get
Left: 380.1327
Right: 50.26548
We must divide each by two because we are only looking for semi-circle which is exactly half the area of a full circle.
Then,
Left: 190.066
Right: 25.1327
190.066+ 25.1327= 215.199 = 215.2ft^2
Answer:
A
Step-by-step explanation:
(y-5) / (7-5) = (x-1) / (2-1)
(y-5) / 2 = x-1
y-5 = 2x -2
y = 2x +3
#1)
A) b = 10.57
B) a = 22.66; the different methods are shown below.
#2)
A) Let a = the side opposite the 15° angle; a = 1.35.
Let B = the angle opposite the side marked 4; m∠B = 50.07°.
Let C = the angle opposite the side marked 3; m∠C = 114.93°.
B) b = 10.77
m∠A = 83°
a = 15.11
Explanation
#1)
A) We know that the sine ratio is opposite/hypotenuse. The side opposite the 25° angle is b, and the hypotenuse is 25:
sin 25 = b/25
Multiply both sides by 25:
25*sin 25 = (b/25)*25
25*sin 25 = b
10.57 = b
B) The first way we can find a is using the Pythagorean theorem. In Part A above, we found the length of b, the other leg of the triangle, and we know the measure of the hypotenuse:
a²+(10.57)² = 25²
a²+111.7249 = 625
Subtract 111.7249 from both sides:
a²+111.7249 - 111.7249 = 625 - 111.7249
a² = 513.2751
Take the square root of both sides:
√a² = √513.2751
a = 22.66
The second way is using the cosine ratio, adjacent/hypotenuse. Side a is adjacent to the 25° angle, and the hypotenuse is 25:
cos 25 = a/25
Multiply both sides by 25:
25*cos 25 = (a/25)*25
25*cos 25 = a
22.66 = a
The third way is using the other angle. First, find the measure of angle A by subtracting the other two angles from 180:
m∠A = 180-(90+25) = 180-115 = 65°
Side a is opposite ∠A; opposite/hypotenuse is the sine ratio:
a/25 = sin 65
Multiply both sides by 25:
(a/25)*25 = 25*sin 65
a = 25*sin 65
a = 22.66
#2)
A) Let side a be the one across from the 15° angle. This would make the 15° angle ∠A. We will define b as the side marked 4 and c as the side marked 3. We will use the law of cosines:
a² = b²+c²-2bc cos A
a² = 4²+3²-2(4)(3)cos 15
a² = 16+9-24cos 15
a² = 25-24cos 15
a² = 1.82
Take the square root of both sides:
√a² = √1.82
a = 1.35
Use the law of sines to find m∠B:
sin A/a = sin B/b
sin 15/1.35 = sin B/4
Cross multiply:
4*sin 15 = 1.35*sin B
Divide both sides by 1.35:
(4*sin 15)/1.35 = (1.35*sin B)/1.35
(4*sin 15)/1.35 = sin B
Take the inverse sine of both sides:
sin⁻¹((4*sin 15)/1.35) = sin⁻¹(sin B)
50.07 = B
Subtract both known angles from 180 to find m∠C:
180-(15+50.07) = 180-65.07 = 114.93°
B) Use the law of sines to find side b:
sin C/c = sin B/b
sin 52/12 = sin 45/b
Cross multiply:
b*sin 52 = 12*sin 45
Divide both sides by sin 52:
(b*sin 52)/(sin 52) = (12*sin 45)/(sin 52)
b = 10.77
Find m∠A by subtracting both known angles from 180:
180-(52+45) = 180-97 = 83°
Use the law of sines to find side a:
sin C/c = sin A/a
sin 52/12 = sin 83/a
Cross multiply:
a*sin 52 = 12*sin 83
Divide both sides by sin 52:
(a*sin 52)/(sin 52) = (12*sin 83)/(sin 52)
a = 15.11
Answer:
perimeter = 6x + 15
Step-by-step explanation:
The perimeter of the triangle is the distance around the triangle.
We need to apply our ability to convert word problems in to mathematical expressions.
We were told that the bottom of the triangle is x units.
From the diagram perimeter 4x + 12 + x + 3 + x = 6x + 15
Four times the length of the bottom will be 4x .
12 more than 4 times the bottom will be 4x + 12.
Hence another side of the triangle is 4x + 12.
Finally we were told that the last side is 3 more than the bottom, that will be x + 3.
