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3 years ago

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Three consecutive odd integers are such that the sum of the first and second is 31 less than 3 times the third. Find the integer

s (URGENT)

1 answer:

Otrada [13]3 years ago

3 0

1st:x

2nd x+2

3rd: x+4

(x)+(x+2) = 3(x+4)-31

distribute

2x+2 = 3x+12-31

2x+2 =3x-19

subtract 2x from each side

2 = x-19

add 19 to each side

21 =x

Answer: 21,23,25

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Answer:

Part A) Yes , the triangles are congruent

Part B) The side-angle-side (SAS) theorem

Part C) The perimeter of ∆PQR is $17\ ft$

Step-by-step explanation:

Step 1

we know that

The side-angle-side (SAS) theorem, states that: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

so in this problem

Traingle PQR and Triangle STU are congruent by the SAS Theorem

because

m<PQR=m<STU -------> included angle

PQ=TS

QR=TU

Step 2

<u>Find the value of y</u>

we know that

If the triangles are congruent

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so

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substitute

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$(3y-y)=(2+4)$

$(2y)=(6)$

$y=3\ ft$

$PR=3y-2=3(3)-2=7\ ft$

$SU=y+4=(3)+4=7\ ft$

so

$PR=SU$

Step 3

Find the perimeter ∆PQR

Remember that

The perimeter of ∆PQR is equal to the perimeter ∆STU

The perimeter is equal to

$P=PQ+QR+PR$

substitute the values

$P=4+6+7=17\ ft$

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