Question

The perimeter of the triangle shown are equal. Find the side lengths of each triangle.

Answer 1

12,16,15 and 12,12,19

Explanation:

Hello, I think I can help you with this.

the perimeter of a triangle is the sum of its three sides

Perimeter = side1+side2+side3

Step 1

Perimeter1=(2x+4)+(2x+3)+2x

P1=2x+4+2x+3+2x

P1=6x+7

Step 2

Perimeter2=2x+2x+(3x+1)

P2=2x+2x+3x+1

P2=7x+1

Step 3

find x,

P1=P2

6x+7=7x+1

7-1=7x-6x

6=x

x=6

Step 4

replace the value of x to find each side length

triangle1(left)

2x=2(6)=12

2x=12

2x+4=12+4=16

2x+4=16

2x+3=12+3=15

2x+3=15

triangle2(right)

2x=2(6)=12

2x=12

3x+1=3(6)+1=18+1=19

3x+1=19.

Have a great day

Answer 2

Good morning ☕️

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Explanation:

Let p1 be the perimeter of triangle ABC

p2 be the perimeter of triangle PQR

p1=(2x+4)+(2x+3)+(2x) = 6x+7

p2=(2x)+(2x)+(3x+1) = 7x+1

p1=p2 ⇔ 6x+7=7x+1 ⇔ 7x-6x=7-1 ⇔x=6

Then :

AC=2(6)=12

AB=2(6)+4=16

BC=2(6)+3=15

PQ=12

QR=12

PR=3(6)+1=19.

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:)