Question

geometric and spatial reasoning:
includes converting units within measurement systems, solving geometric problems (perimeter, area,
surface area, and volume), performing transformations, and applying right triangle trigonometry.

1. if the length l of a rectangle is 17 less than twice the width w, which of the following gives the length of the

rectangle in terms of the width?
a. ( l = 17 - 2w )
b. ( l = 2w - 17 )
c. ( l = 17w - 2 )
d. ( l = 2 - 17w )

1. the formula for the perimeter of a rectangle with length l and width w is given below. if a rectangle has a

perimeter 42, what could be its length l and width w?
( p = 2(l + w) )
a. ( l = 10, w = 32 )
b. ( l = 21, w = 21 )
c. ( l = 12, w = 13 )
d. ( l = 14, w = 7 )

1. if a triangle has sides of length ( x, x + 2 ), and ( x - 1 ), what is the perimeter of the triangle in terms of x?

a. ( 3x - 3 )
b. ( 3x - 1 )
c. ( 3x + 1 )
d. ( 3x + 3 )

1. what is the area of a square that has a perimeter of 32 feet?

a. 28 square feet
b. 36 square feet
c. 49 square feet
d. 64 square feet

1. figure 2 is a ( 90^{circ} ) clockwise rotation of figure 1. which of the following angles in figure 2 corresponds to

in figure 1?
a. ( angle w )
b. ( angle x )
c. ( angle y )
d. ( angle z )

Explanation:

Step1: Analyze question 11

The length \(L\) is 17 less than twice the width \(W\). Twice the width is \(2W\), and 17 less than that is \(2W - 17\).

Step2: Analyze question 12

Use the perimeter formula \(P = 2(L + W)\). For option D: \(L = 14\), \(W = 7\). Then \(2(14 + 7)=2\times21 = 42\).

Step3: Analyze question 13

The perimeter of a triangle is the sum of its sides. \(P=x+(x + 2)+(x - 1)=x+x + 2+x - 1=3x+1\).

Step4: Analyze question 14

For a square, perimeter \(P = 4s\) (where \(s\) is the side length). Given \(P = 32\), then \(4s=32\), so \(s = 8\). Area \(A=s^{2}=8^{2}=64\).

Answer:

1. B. \(L = 2W - 17\)
2. D. \(L = 14\), \(W = 7\)
3. C. \(3x + 1\)
4. D. 64 square feet