Solve the problem.
-Consider the figure below. (a) Write an expression for the length of the top. (b) Write an expression for the length of the left side. (c) Write an expression for the area of the largest rectangle.
A) +35z
B) + 8z + 72
C) + 35z + 72
D) + 27z +72

Question

Solve the problem.
-Consider the figure below. (a) Write an expression for the length of the top. (b) Write an expression for the length of the left side. (c) Write an expression for the area of the largest rectangle. 
A) +35z 
B) + 8z + 72 
C) + 35z + 72 
D) + 27z +72

Quizplus · Accepted Answer

(a) The length of the top is equal to the sum of the length of the bottom (35z) and the width of the smaller rectangle (72), which is (35z+72).
(b) The length of the left side is equal to the length of the larger rectangle minus the height of the smaller rectangle, which is (11z+72-8z) or (3z+72).
(c) The largest rectangle can be formed by combining the two smaller rectangles. Its area is equal to the product of its length and width, which is ((35z+72)*(3z+72)) or (11z^2 + 231z + 5184). However, this expression can be factored further as (11z+144)*(z+36), so the area can also be expressed as (11z+144)*(z+36).

Out of the choices given, only option C matches both (a) and (c), which are (35z+72) for the length of the top and (11z+144)*(z+36) for the area of the largest rectangle. Option B is close, but it incorrectly gives an expression of (8z+72) for the height of the smaller rectangle instead of (8z), which affects the expression for the length of the left side. Option A and D give incorrect expressions for both (a) and (c). (a) The length of the top can be found by adding the length of the horizontal line segment on the left (which is 35z), the length of the diagonal line segment (which is also 35z), and the length of the horizontal line segment on the right (which is 2z). Therefore, the expression for the length of the top is 35z + 35z + 2z = 72z.

(b) The length of the left side can be found by adding the length of the vertical line segment on the left (which is 8z), the length of the diagonal line segment (which is also 8z), and the length of the vertical line segment on the right (which is 27z). Therefore, the expression for the length of the left side is 8z + 8z + 27z = 43z.

(c) The area of the largest rectangle can be found by multiplying the length of the top by the length of the left side. Therefore, the expression for the area of the largest rectangle is (35z+35z+2z)*(8z+8z+27z) = (72z)*(43z) = 3096z^2.

Option C is the correct choice as it matches all the expressions.

Solve the Problem