Triangle ABC-Triangle DEF are their areas are respectively 49cm2 and 100cm2 if DE is 17.5 then find AB
Answers
The length of AB is 12.25 cm.
Step-by-step explanation:
It is given that,
∆ABC ~ ∆DEF
Area of ∆ABC = 49 cm²
Area of ∆DEF = 100 cm²
DE = 17.5 cm
Now, we know that when the two given triangles are similar, then the ratio of there areas is equal to the ratio of the square of their corresponding sides.
∴ [Area of the ΔABC] / [Area of the ΔDEF] = [AB²]/[PQ²]
substituting the given values
⇒ 49/100 = AB²/(17.5)²
⇒ AB² = [49 * 306.25] / 100
⇒ AB = √[15006.25/100]
⇒ AB = √[150.0625]
⇒ AB = 12.25 cm
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