Perimeter From Diagrams
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ISEE Lower Level: Mathematics Achievement › Perimeter From Diagrams
A large rectangle is 20 feet long and 10 feet wide. A smaller rectangular porch that is 6 feet long and 4 feet wide juts out from the middle of one of the 20-foot sides. What is the perimeter of the combined shape of the house and porch?
60 feet
68 feet
80 feet
88 feet
Explanation
Start with the perimeter of the large rectangle: 2 * (20 + 10) = 60 feet. When the porch is added, a 6-foot section of the house's wall is replaced by the three outer walls of the porch. The lengths of these three walls are 4 feet, 6 feet, and 4 feet. The change to the perimeter is -6 (the removed wall section) + 4 + 6 + 4 = +8 feet. The new total perimeter is 60 + 8 = 68 feet.
A rectangular poster has a width of 10 inches. Its length is 4 inches greater than its width. What is the perimeter of the poster?
34 inches
24 inches
48 inches
140 inches
Explanation
First, determine the length of the poster. The width is 10 inches, and the length is 4 inches greater, so the length is 10 + 4 = 14 inches. The perimeter of a rectangle is P = 2 × (length + width). So, P = 2 × (14 + 10) = 2 × 24 = 48 inches.
A rectangular backyard is 25 feet long and 18 feet wide. The entire yard is enclosed by a fence, but there is a 3-foot wide gate in the fence. How many feet of fencing material were used, not including the gate?
83 feet
89 feet
86 feet
450 feet
Explanation
First, calculate the total perimeter of the backyard: P = 2 × (25 + 18) = 2 × 43 = 86 feet. The gate is part of this perimeter, but it is not made of fencing material. So, subtract the width of the gate from the total perimeter: 86 feet - 3 feet = 83 feet. Therefore, 83 feet of fencing material were used.
A triangle has a perimeter of 30 feet. The second side is 2 feet longer than the first side. The third side is 4 feet longer than the first side. What is the length of the shortest side?
10 feet
8 feet
24 feet
12 feet
Explanation
Let the shortest side be 'x'. The other sides are 'x + 2' and 'x + 4'. The perimeter is the sum of the sides: x + (x + 2) + (x + 4) = 30. This simplifies to 3x + 6 = 30. Subtract 6 from both sides: 3x = 24. Divide by 3: x = 8. The shortest side is 8 feet.
A square has a side length of 8 cm. A rectangle has a length of 10 cm and a width of 5 cm. What is the difference between the perimeter of the square and the perimeter of the rectangle?
2 cm
14 cm
34 cm
62 cm
Explanation
First, find the perimeter of the square: P_square = 4 × 8 cm = 32 cm. Next, find the perimeter of the rectangle: P_rectangle = 2 × (10 cm + 5 cm) = 2 × 15 cm = 30 cm. The difference is 32 cm - 30 cm = 2 cm.
A shape is made by joining three identical squares in a row, side to side. If the side of each square is 4 centimeters, what is the perimeter of the entire shape?
48 cm²
32 cm
24 cm
48 cm
Explanation
The shape is a long rectangle composed of three squares. The top side has a length of 4+4+4=12 cm. The bottom side also has a length of 12 cm. The left and right sides each have a length of 4 cm. The perimeter is the sum of the outside edges: 12 + 12 + 4 + 4 = 32 cm. Alternatively, there are 8 exterior sides of length 4 cm, so 8 x 4 = 32 cm.
A square garden has a side length of 15 feet. A brick path that is 3 feet wide is built around the entire outside of the garden. What is the perimeter of the outer edge of the brick path?
84 feet
72 feet
60 feet
96 feet
Explanation
The garden is a 15-foot square. The 3-foot path adds 3 feet to the top, bottom, left, and right. The new, larger square (garden plus path) has a side length of 15 + 3 + 3 = 21 feet. The perimeter of this new square is 4 × 21 = 84 feet.
A rectangular field has a length of 30 meters and a width of 20 meters. A farmer walks around the entire edge of the field one time. What is the total distance the farmer walks?
100 meters
600 meters
50 meters
300 meters
Explanation
The distance around the edge of a field is its perimeter. The formula for the perimeter of a rectangle is P = 2 × (length + width). In this case, P = 2 × (30 meters + 20 meters) = 2 × (50 meters) = 100 meters. The farmer walks 100 meters.
A rectangular photograph is 7 inches wide and 9 inches tall. It is placed in a frame that adds a border of 2 inches to every side. What is the perimeter of the outside edge of the framed photograph?
32 inches
77 inches
48 inches
40 inches
Explanation
The frame adds 2 inches to each side. The new width is 7 + 2 + 2 = 11 inches. The new height is 9 + 2 + 2 = 13 inches. The perimeter of the outside of the frame is P = 2 × (11 + 13) = 2 × 24 = 48 inches.
An L-shaped room has six walls. The outside wall measurements are 12 feet, 15 feet, 7 feet, 6 feet, 5 feet, and 9 feet. What is the perimeter of the room?
49 feet
34 feet
90 feet
54 feet
Explanation
The perimeter of a shape is the sum of the lengths of all its sides. To find the perimeter of the L-shaped room, add all the given wall measurements: 12 + 15 + 7 + 6 + 5 + 9 = 54 feet.