Question

1 si 2, va rog,
1. In figura alaturata [AF]≡[FE]≡[ED]≡[DB] si FI║EH║DG║BC. Daca BC = 12cm, calculati EH,FI DG.

2.Determinati x ∈N din urmatoarele figuri:


Va rog este URGENT!

Answer 1

Explicație pas cu pas:

1. Triunghiuri asemenea

$\frac{af}{ab} = \frac{fi}{bc} \\ af + fe + ed + db = ab \\ 4af = ab = > af = \frac{ab}{4} \\ \frac{ab}{4} \times \frac{1}{ab} = \frac{fi}{12} \\ \frac{1}{4} = \frac{fi}{12} \\ fi = 3 \\ \frac{ae}{ab} = \frac{eh}{bc} \\ \frac{ab}{2} \times \frac{1}{ab} = \frac{eh}{12} \\ eh = 6 \\ \frac{ad}{ab} = \frac{dg}{bc} \\ \frac{3}{4} ab \times \frac{1}{ab} = \frac{dg}{12} \\ dg = 9$

2. Triunghiuri asemenea

$\frac{15}{15 + x - 2} = \frac{2x + 3}{2x + 3 + 4} \\ 15(2x + 7) = (x + 13)(2x + 3) \\ 30x + 105 = 2 {x}^{2} + 3x + 26x + 39 \\ 105 = 2 {x}^{2} - x + 39 \\ 2 {x}^{2} - x - 66 = 0 \\ (x - 6)(2x + 11) = 0 \\ x = 6$

3.

$\frac{3x + 1}{2x + 3x + 1} = \frac{15}{3x + 15} \\ (3x + 1)(3x + 15) = 15(5x + 1) \\ 9 {x}^{2} + 45x + 3x + 15 = 75x + 15 \\ 9 {x}^{2} - 27x = 0 \\ 9x(x - 3) = 0 \\ x = 3$