A triangle has side lengths of left parenthesis, q, plus, r, right parenthesis(q+r) centimeters, left parenthesis, 5, q, minus, 10, s, right parenthesis(5q−10s) centimeters, and left parenthesis, 5, s, minus, 7, r, right parenthesis(5s−7r) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
Question
A triangle has side lengths of left parenthesis, q, plus, r, right parenthesis(q+r) centimeters, left parenthesis, 5, q, minus, 10, s, right parenthesis(5q−10s) centimeters, and left parenthesis, 5, s, minus, 7, r, right parenthesis(5s−7r) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
Solution
The perimeter of a triangle is the sum of the lengths of all its sides.
Given that the sides of the triangle are (q+r) cm, (5q−10s) cm, and (5s−7r) cm, we can find the perimeter by adding these three expressions together.
So, the perimeter P of the triangle is:
P = (q + r) + (5q - 10s) + (5s - 7r)
This simplifies to:
P = 6q - 6r - 5s
So, the expression that represents the perimeter of the triangle in centimeters is 6q - 6r - 5s.
Similar Questions
The width of a rectangle measures left parenthesis, 5, r, plus, 8, s, right parenthesis(5r+8s) centimeters, and its length measures left parenthesis, 7, r, minus, 7, s, right parenthesis(7r−7s) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
The longest side of a triangle is a cm. (3)The second side is b cm shorter than the first side.The third side is half as long as the second side.Write an expression, in its simplest form, for the perimeter ofthe triangle. Show your working.
The ratio of the side lengths of 2 similar triangles is 3:5. The smaller triangle has sides that measure 5 centimeters, 7 centimeters, and 9 centimeters. What is the perimeter, in centimeters, of the larger triangle?Responses1235123512 and 3 fifths212121353535636363105
The width of a rectangle measures left parenthesis, 9, v, minus, 5, w, right parenthesis(9v−5w) centimeters, and its length measures left parenthesis, 9, v, plus, 6, w, right parenthesis(9v+6w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
The lengths of the sides of a triangle are in the ratios 2 : 6 : 7The length of the longest side of the triangle is 24.5 cm.Work out the perimeter of the triangle.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.