∆ABC~∆DEF area of triangle abc is 64cm² and area of triangle DEF is 9cm². if AB is 16cm what is De?
∆ABC~∆DEF area of triangle abc is 64cm² and area of triangle DEF is 9cm². if AB is 16cm what is De?
In this solution, we assume that the given sides of ∆ABC and ∆DEF correspond to each other. So, the side DE is equal to 6 cm.
Since ∆ABC ~ ∆DEF, the corresponding sides of the triangles are proportional to each other, from that the following proportion can be done:
AB/DE = BC/EF
By substituting the given values, we get:
16/DE = √(64/9)
To simplify the equation, we have to square both the sides:
(16/DE)² = 64/9
By Cross-multiplying, we get:
256 = 64(DE)²/9
By simplifying further, we have:
(DE)² = (256 × 9)/64
(DE)² = 36
By taking the square root of both sides, we get:
DE = √36
DE = 6 cm
Therefore, the DE is equal to 6 cm.
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