Question

ABCD is a rhombus with A = 60° , BC = (3x+5)cm , CD =(6x-10)cm and AC =(3y-1)cm. Find

x and y.

please urgent please
no incorrect answers please​

Answer 1

Solution :-

Fig(i) from image :-

→ BC = CD .(All sides of rhombus are equal in length.)

So,

→ 3x + 5 = 6x - 10

→ 6x - 3x = 5 + 10

→ 3x = 15

dividing both sides by 5,

→ x = 5. (Ans.)

Than ,

Each side of rhombus = 3x + 5 = 3*5 + 5 = 20cm.

Now, in ∆DAB,

→ ∠DAB = 60° (given) .

→ DA = AB. (sides of rhombus are equal.)

So,

→ ∠ABD = ∠ADB = 60° . (Angle opp. to equal sides are also equal.)

therefore,

→ Diagonal BD is equal to sides of rhombus .(All angles 60° that means ∆DAB is an equilateral ∆.}

hence,

→ ∆BCD is also an equilateral ∆.

∴

→ ∠ADC = 60° + 60° = 120° .

Taking fig(2) from image now :-

in ∆ADC we have,

→ AD = DC = 20cm.

→ ∠ADC = 120° .

we know that, by cosine rule,

• AC² = AD² + DC² - 2 * AD * DC * cos(∠ADC)

Putting all values we get,

→ AC² = (20)² + (20)² - 2 * 20 * 20 * cos(120°)

→ AC² = 400 + 400 - 800 * (-1/2)

→ AC² = 800 + 400

→ AC² = 1200

→ AC² = (400 * 3)

→ AC = 20√3 cm.

Therefore,

→ 3y - 1 = 20√3

→ 3y = (20√3 + 1)

→ y = (20√3 + 1)/3 (Ans.)

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Answer 2

Answer:

thanks for free points.