1) Since triangle ABD is a right triangle where lengths of the two shorter sides are in the ratio of 4 to 3, the triangle must be a 3-4-5 right triangle (a common right-triangle type).
2) We can find the length of AD. AB = 3 × 2 = 6 BD = 4 × 2 = 8 Therefore, AD = 5 × 2 = 10.
3) Since AE + ED = AD, AE + 5 = 10
4) AE must equal 5.
The correct answer is choice (C). ---------- I used this formula. Area of a triganle will be A = (1/2)bh. And we know BD = 8, AB = 6, ED = 5. Therefore Area = 1/2 × 8 × 6 = 24. We need the parameter of the diagram which is P = BD + AB + ED + AE, AE is unknown. P = 8 + 6 + 5 + AE. However we know the area of the entire diagram. From adding the parimteter p = 8 + 6 + 5 = 19 Subtracting perimeter from Area 24 – 19 = 5 this will represent AE. Therefore, AE = 5.
I know this can be represented in a better way or correct way.. Thank you...
Could this answer not have been found through calculating the hypotenuse of ABD, and then subtract ED from the result?
That's exactly what we did. We calculated the hypotenuse of ABD using the property of the 3-4-5 right triangle (You can use the Pythagorean theorem instead). It equals 10. Then we subtracted ED, which equals 5, and calculated the length of AE: 10 – 5 = 5.
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