Question

1. For the shown triangle, AD is 42, MD is 27, AN is 20 and NG is 3x+3.

Answer 1

x = 11

Explanation:

Since the given triangle are proportional to each other. So,

AM/AD = AN/AG

(AD - MD)/AD = AN/(AN + NG)

=> (42 - 27)/42 = 20/(20 + 3x + 3)

=> 15/42 = 20/23 + 3x

=> 15(23 + 3x) = 42(20)

=> 345 + 45x = 840

=> 45x = 840 - 345

=> 45x = 495

=> x = 495/45

=> x = 11

Answer 2

• 11

Explanation:

According to triangle similarity, corresponding sides have equal ratios.

• AM/AD = AN/AG

Convert the ratio as below:

• (AD - MD)/AD = AN/(AN + NG)
• (42 - 27)/42 = 20/(20 + 3x + 3)

Simplify and solve for x:

• 15/42 = 20/(3x + 23)
• 5/14 = 20/(3x + 23)
• 1/14 = 4/(3x + 23)
• 3x + 23 = 4*14
• 3x + 23 = 56
• 3x = 33
• x = 11