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In the figure above,
at point B. If AE = 16, how many times greater is the area of ΔDBE than the area of ΔABC?Correct answer is '9'. Can you explain this answer?
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In the figure above, at point B. If AE = 16, how many times greater is...
Because AC and DE are parallel, we can establish three pairs of congruent angles:
∠ABC ≌ ∠DBE (vertical angles)
∠ACD ≌∠CDE (alternate interior angles)
∠DEA ≌ ∠EAC (alternate interior angles)
Therefore the two triangles are similar, and all pairs of corresponding sides are proportional. If the ratio of corresponding sides in two similar figures is m : n, the ratio of areas of the two figures must by m2 : n2'. If AE = 16, then BE = 16 - 4 = 12, and therefore BE : AB = 12 : 4 = 3 : 1. Since the sides of ΔDBE are 3 times greater than the corresponding sides of ΔABC, the area of ΔDBE must be 32 = 9 times greater than the area of ΔABC.
∠ABC ≌ ∠DBE (vertical angles)
∠ACD ≌∠CDE (alternate interior angles)
∠DEA ≌ ∠EAC (alternate interior angles)
Therefore the two triangles are similar, and all pairs of corresponding sides are proportional. If the ratio of corresponding sides in two similar figures is m : n, the ratio of areas of the two figures must by m2 : n2'. If AE = 16, then BE = 16 - 4 = 12, and therefore BE : AB = 12 : 4 = 3 : 1. Since the sides of ΔDBE are 3 times greater than the corresponding sides of ΔABC, the area of ΔDBE must be 32 = 9 times greater than the area of ΔABC.
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In the figure above, at point B. If AE = 16, how many times greater is the area of ΔDBE than the area of ΔABC?Correct answer is '9'. Can you explain this answer?
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In the figure above, at point B. If AE = 16, how many times greater is the area of ΔDBE than the area of ΔABC?Correct answer is '9'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about In the figure above, at point B. If AE = 16, how many times greater is the area of ΔDBE than the area of ΔABC?Correct answer is '9'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the figure above, at point B. If AE = 16, how many times greater is the area of ΔDBE than the area of ΔABC?Correct answer is '9'. Can you explain this answer?.
In the figure above, at point B. If AE = 16, how many times greater is the area of ΔDBE than the area of ΔABC?Correct answer is '9'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about In the figure above, at point B. If AE = 16, how many times greater is the area of ΔDBE than the area of ΔABC?Correct answer is '9'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the figure above, at point B. If AE = 16, how many times greater is the area of ΔDBE than the area of ΔABC?Correct answer is '9'. Can you explain this answer?.
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