Mathematics, 04.08.2019 09:30 hgfddfg

Atrapezoid has a perimeter of 117cm. the two shortest sides have the same length. the third side is 12cm longer than one short side. the final side is 9cm less than three times one short side. how long is each side of the trapezoid?

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Answers

First, make an equation system for the problem

An equation for "A trapezoid has a perimeter of 117cm" is
⇒ s₁ + s₂ + s₃ + s₄ = 117
"two shortest side is the same"
2s₁ + s₃ + s₄ = 117

An equation for "the third side is 12cm longer than one short side"
⇒ s₃ = s₁ + 12

An equation for "the final side is 9cm less than three times one short side"
⇒ s₄ = 3s₁ - 9

Second, solve the problem by subtitution method.
Subtitute s₃ with s₁+12 and subtitute s₄ with 3s₁-9
2s₁ + s₃ + s₄ = 117
2s₁ + (s₁ + 12) + (3s₁ - 9) = 117
6s₁ + 3 = 117
6s₁ = 117 - 3
6s₁ = 114
s₁ = 114/6
s₁ = 19
The length of two shortest sides each is 19 cm

Find the third side
s₃ = s₁ + 12
s₃ = 19 + 12
s₃ = 31
The length of third side is 31 cm

Find the fourth side
s₄ = 3s₁ - 9
s₄ = 3(19) - 9
s₄ = 57 - 9
s₄ = 48
The length of fourth side is 48 cm

ANSWER:
The lengths of the sides are 19 cm, 19 cm, 31 cm + 48 cm

Answer from: Quest

none of the above.

for one of the equations to be used in the process, there has to be a $2x^2$ term in the equation since $2x$ squared is $2x^2$ .

since there is only a $x^2$ term in the first equation, we cannot derive a $2x+4$ from completing the square.

solving with completing the square

$x^2=-4x+3$

$x^2+4x=3$

$x^2+4x+4=7$

$(x+2)^2=7$

$x+2=+-\sqrt{7}$

$x=2+-\sqrt{7}$

Answer from: Quest

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

$a=9\times 12=108\text {ft^2}$

so the area of the floor is 108 square feet, converting that into square yards we get,

$108 \times 0.1111= 12 \text{yd^2}$

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

$\$15 \times 12=\$180$

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

$a = 12 \times 15=180\text {ft}^2$

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

$180 \times 0.111=20 \text {yd}^2$

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

$\$15 \times 20= \$300$

so, it will cost $300.

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Atrapezoid has a perimeter of 117cm. the two shortest sides have the same length. the third side is...

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