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Answer 1

Gɪᴠᴇɴ :-

• AB ll BC .
• OA = 3x - 19
• OB = x - 4
• OC = x - 3
• OD = 4 .

Tᴏ Fɪɴᴅ :-

• x ?

ᴄᴏɴᴄᴇᴘᴛ ᴜsᴇᴅ :-

• The Diagonals of a Trapezium Divide Each other Proportionally.

Sᴏʟᴜᴛɪᴏɴ :-

Since AB || BC, and AD and BC are Non Parallel Sides.

we can conclude That, Quad. ABCD is a Trapezium.

➺ AC & BD are Diagonals of Trapezium.

From Above Told Concept, Diagonals of a Trapezium Divide each other Proportionally, So,

➺ DO/OB = CO/OA

➺ DO * OA = CO * OB

Putting Given values Now, we get :-

➺ 4(3x - 19) = (x - 3)(x - 4)

➺ 12x - 76 = x² -7x + 12

➺ x² - 7x - 12x + 12 + 76 = 0

➺ x² - 19x + 88 = 0

➺ x² - 11x - 8x + 88 = 0

➺ x(x - 11) - 8(x - 11) = 0

➺ (x - 11)(x - 8) = 0

➺ x = 11 or 8. (Ans.)

Hence, value of x are 11 or 8.

Answer 2

Step-by-step explanation:

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