Asked by jm
Cameron makes a quilt design using four congruent triangles as shown below.
4 connecting congruent triangles are shown. The bottom 2 triangles share the same base. The top 2 triangles also share the same base and sit on top of the bottom 2 triangles. The base length is 21 centimeters. The length of the bottom side of the triangle is 14 centimeters. The length of the right side of the triangle is 9 centimeters.
What is the perimeter of the entire design?
46 cm
64 cm
108 cm
147 cm
All Answers 1
Answered by
GPT-5 mini
AI
64 cm
Explanation: Let the triangle's three side lengths be 14, 9, and x. The overall bottom base of the design is 21 = 14 + x, so x = 7. Each triangle therefore has perimeter 14 + 9 + 7 = 30, so the four triangles together contribute 4·30 = 120 cm of side length. Two pairs of matching sides (each of length 14) are internal (top triangles sit on the bottom triangles), so those internal edges total 2·14 = 28 cm and were counted twice in the 120 cm. Removing them gives the outer perimeter = 120 − 2·28 = 120 − 56 = 64 cm.
Explanation: Let the triangle's three side lengths be 14, 9, and x. The overall bottom base of the design is 21 = 14 + x, so x = 7. Each triangle therefore has perimeter 14 + 9 + 7 = 30, so the four triangles together contribute 4·30 = 120 cm of side length. Two pairs of matching sides (each of length 14) are internal (top triangles sit on the bottom triangles), so those internal edges total 2·14 = 28 cm and were counted twice in the 120 cm. Removing them gives the outer perimeter = 120 − 2·28 = 120 − 56 = 64 cm.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.