Mathematics
Find the perimeter of a triangle whose sides are 2y + 3z, z - y, 4y - 2z.
Algebraic Expressions
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Answer
Given:
Side 1 = 2y + 3z
Side 2 = z - y
Side 3 = 4y - 2z
Perimeter of a triangle = Side 1 + Side 2 + Side 3
Substituting the values above, we get:
Perimeter of a triangle = (2y + 3z + z - y + 4y - 2z)
= (2y - y + 4y) + (3z + z - 2z) [Grouping like terms]
= (2 - 1 + 4)y + (3 + 1 - 2)z [Combining coefficients]
= 5y + 2z
The perimeter of the triangle is 5y + 2z.
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The two adjacent sides of a rectangle are 3a - b and 6b - a. Find its perimeter.
Subtract:
(i) 3a - 2b + 4c from 5a - 3b - 5c
(ii) 5x2 - 3xy - 7y2 from 3x2 - xy - 2y2
(iii) 3p3 - 5p2q + 2q2 from q2 + p2q - 4p3
(iv) ab - bc - ca from 3ab + 2bc - 4ca
(v) 3z3 - 2z2 + 7z - 8 from 8 - z - z2
(vi) 2abc - a2 - b2 from b2 + a2 - 2abc
(i) Subtract 6x3 - 5x2 + 4x - 3 from the sum of x + 2x2 - 3x3 and 2 - x2 + 6x - x3.
(ii) Subtract the sum of a + 2b - 3c and 2c - 3b - 4a from the sum of 5b - 4c + a and 2c - 3b - 4a.
(iii) Subtract the sum of x2 - 5xy + 2y2 and y2 - 2xy - 3x2 from the sum of 6x2 - 8xy - y2 and 2xy - 2y2 - x2.