Ask Question
13 March, 04:37

Solve for x. Enter your answer in the box. x = A triangle with vertices labeled as A, C, D. Side C D is the base and the top vertex is A. Side C D is parallel to B E. Side A E is labeled as 7x minus 40, side E D is labeled as 18, side C B is labeled as 15, and side A B is labeled as 25.

+5
Answers (1)
  1. 13 March, 08:14
    0
    x = 10

    Step-by-step explanation:

    In ΔADC

    ∵ EB / / DC

    ∴ m∠AEB = m∠ADC ⇒ corresponding angles

    ∴m∠ABE = m∠ACD ⇒ corresponding angles

    In the two triangles ADC, AEB

    ∵ m∠AEB = m∠ADC

    ∵ m∠ABE = m∠ACD

    ∵ ∠A is a common angle

    ∴ ΔADC similar to ΔAEB

    ∴ AE/AC = AB/AC

    ∵ AE = 7x - 40, ED = 18

    ∴ AD = 7x - 40 + 18 = 7x - 22

    ∵ AB = 25, BC = 15

    ∴ AC = 25 + 15 = 40

    ∴ (7x - 40) / (7x - 22) = 25/40 ⇒ use cross multiplication

    ∴ 40 (7x - 40) = 25 (7x - 22)

    ∴ 280x - 1600 = 175x - 550

    ∴ 280x - 175x = 1600 - 550

    ∴ 105x = 1050

    ∴ x = 1050 : 105 = 10
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Solve for x. Enter your answer in the box. x = A triangle with vertices labeled as A, C, D. Side C D is the base and the top vertex is A. ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers