Question
Download Solution PDFΔABC ~ ΔDEF and the perimeters of these triangles are 32 cm and 12 cm, respectively. If DE = 6 cm, then what will be the length of AB?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
ΔABC ~ ΔDEF and the perimeters of these triangles are 32 cm and 12 cm.
DE = 6 cm
Concept used:
1. If two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion
2. The perimeter of a triangle is the sum of all its sides.
Calculation:
According to the question,
(AB + BC + AC) = 32 ....(1)
(DE + EF + DF) = 12 ....(2)
Since ΔABC ~ ΔDEF,
From 1,
(AB + BC + AC) = 32
⇒ K(DE + EF + DF) = 32
⇒ K × 12 = 32
⇒ K = 32/12
⇒ K = 8/3
Now, AB
⇒ 8/3 × DE
⇒ 8/3 × 6 = 16 cm
∴ The length of AB is 16 cm.
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