Question
The ratio of the perimeter of triangle PQR to the perimeter of rectangle ABCD is 5 : 9. All in centimeters
Triangle (sides) PQ: (x-3) PR: (3x-5) QR: (4x+3)
Rectangle (sides) AB: (2x+2) BC: (4x - 1/2) [AB is longer than BC]
a. Write algebraic expressions for the perimeters of triangle PQR and rectangle ABCD.
b. Write a linear equation using the algebraic expressions written in part a. Then solve for x.
c. Find the area of rectangle ABCD.
Triangle (sides) PQ: (x-3) PR: (3x-5) QR: (4x+3)
Rectangle (sides) AB: (2x+2) BC: (4x - 1/2) [AB is longer than BC]
a. Write algebraic expressions for the perimeters of triangle PQR and rectangle ABCD.
b. Write a linear equation using the algebraic expressions written in part a. Then solve for x.
c. Find the area of rectangle ABCD.
Answers
[ (x-3) + (3x-5) + (4x+3) ] : [2(2x+2)+ 2(4x - 1/2) ] = 4 : 9
(8x-5) / (12x+3) = 4/9
take over
(8x-5) / (12x+3) = 4/9
take over
so what is the answers
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I'm sorry, but I need more information about what answers you are looking for. Could you please clarify your question?
The ratio of the perimeter of triangle PQR to the perimeter of rectangle ABCD is 5 : 9. All in centimeters
Triangle (sides) PQ: (x-3) PR: (3x-5) QR: (4x+3)
Rectangle (sides) AB: (2x+2) BC: (4x - 1/2) [AB is longer than BC]
a. Write algebraic expressions for the perimeters of triangle PQR and rectangle ABCD.
b. Write a linear equation using the algebraic expressions written in part a. Then solve for x.
c. Find the area of rectangle ABCD.
Triangle (sides) PQ: (x-3) PR: (3x-5) QR: (4x+3)
Rectangle (sides) AB: (2x+2) BC: (4x - 1/2) [AB is longer than BC]
a. Write algebraic expressions for the perimeters of triangle PQR and rectangle ABCD.
b. Write a linear equation using the algebraic expressions written in part a. Then solve for x.
c. Find the area of rectangle ABCD.
a. Perimeter of triangle PQR = (x-3) + (3x-5) + (4x+3) = 8x-5 cm
Perimeter of rectangle ABCD = 2(2x+2) + 2(4x - 1/2) = 12x+3 cm
b. The linear equation using the given ratio of perimeters is:
(8x-5)/(12x+3) = 5/9
Cross-multiplying and simplifying, we get:
72x - 45 = 60x + 15
12x = 60
x = 5
Therefore, the value of x is 5.
c. The area of rectangle ABCD is:
Area = AB x BC
Area = (2x+2) x (4x - 1/2)
Area = 8x^2 + 3x - 1 cm^2
Substituting the value of x as 5, we get:
Area = 203 cm^2
Therefore, the area of rectangle ABCD is 203 square centimeters.
Perimeter of rectangle ABCD = 2(2x+2) + 2(4x - 1/2) = 12x+3 cm
b. The linear equation using the given ratio of perimeters is:
(8x-5)/(12x+3) = 5/9
Cross-multiplying and simplifying, we get:
72x - 45 = 60x + 15
12x = 60
x = 5
Therefore, the value of x is 5.
c. The area of rectangle ABCD is:
Area = AB x BC
Area = (2x+2) x (4x - 1/2)
Area = 8x^2 + 3x - 1 cm^2
Substituting the value of x as 5, we get:
Area = 203 cm^2
Therefore, the area of rectangle ABCD is 203 square centimeters.
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