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Andreas93 [3]
3 years ago
5

The surface area of a rectangular prism is 442 square feet. The length is 11 feet, and the height is 8 feet. What is the width o

f the prism?
I need an explanation please on how to work this problem.
Mathematics
2 answers:
Orlov [11]3 years ago
7 0
There are 6 surfaces on a rectangular prism . 3 pairs of equal area.

Surface area  2wl + 2hw + 2 hl     where h = height, w = width,  l = length.

So inserting the given values:-

442 = 2*w*11 + 2 *8* w + 2*8*11

442 = 22w  + 16w + 176

38w =  442-176 = 266

w =  7

width = 7 feet
Anuta_ua [19.1K]3 years ago
5 0
Formula for the surface area of a rectangular prism is S=2ab + 2bc + 2ac (a-lenght,b-width,c-height).
We need to calculate b (width).
S=442 ft^2
a=11 ft
c=8ft
------------------
b=?

S=2ab + 2bc + 2ac
S=2b(a+c) + 2ac
2b(a+c)=S - 2ac
b=(S - 2ac)/(2(a+c))
b=(442 - 2×11×8)/(2×(11+8))
b=(442 - 176)/(2×19)
b=266/38
b=7 ft
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1. Consider the right triangle ABC given below.
lbvjy [14]
#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
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A car traveling at a rate of 54 miles per hour. What is the car's rate in feet per secondHow many fect will the car travel in 2
Lena [83]

The car's speed in feets per second is 79.2, Hence, it will cover a distance of 158.4 feets in 2 seconds.

Car's speed in miles per hour = 54 miles per hour

Recall :

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Car's rate in feet per second

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