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adell [148]
3 years ago
10

Find x step by step ​

Mathematics
2 answers:
11111nata11111 [884]3 years ago
4 0

Answer:

\frac{4 + (x + 1)}{x + 1}  =  \frac{16}{12}  \\  \\  \frac{5 + x}{x + 1}  =  \frac{16}{12}  \\  \\ 12(5 + x) = 16(x + 1) \\ 60 + 12x = 16x + 16 \\ 4x = 44 \\ x = 11

blagie [28]3 years ago
4 0

Answer:

x = 11 cm

Step-by-step explanation:

Segments DE and BC are parallel (that's what the arrows tell you), so there are two similar triangles formed.

\triangle{ADE} \sim \triangle{ABC}

Corresponding sides are in proportion, so

\frac{AD}{AB}=\frac{12}{16}

The length of AB is (x + 1) + 4 = x + 5, and 12/16 simplifies to 3/4, so

\frac{x+1}{x+5}=\frac{3}{4}

"Cross multiply" to get

4(x+1)=3(x+5)\\4x+4=3x+15\\4x=3x+11\\x=11

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