Question

the angles of a triangle are in the ratio 2:3. If 4 is added to each numbers the new ratio becomes 5:11, what are the numbers?​

Answer 1

Answer:

34, 70

Step-by-step explanation:

Let, the two numbers are x and y.

According to the first conditions,

y+2x+2=21⇒2x−y=−2⟶(1)

and according to the second condition,

y−4x−4=115⇒11x−5y=24⟶(2)

Multiplying equation (1) by 5 we get,

10x−5y=−10⟶(3)

Subtracting equation (2) from equation (3),

⇒11x−5y−10x+5y=24+10

⇒x=34

Putting the value of x in equation (1),

⇒2×34−y=−2⇒68−y=−2⇒y=70

Hence, the required numbers are 34,70.

Answer 2

Answer:

Given,

Ratio of angle of triangle = 2:3

Let the two numbers are 2x and 3x.

If 4 be added to each number, they are in the ratio 5:11.

∴ $\frac{2x+4}{3x+4} =\frac{5}{11}$

  $(2x+4)11=(3x+4)5$

  $22x+44=15x+20$

  $22x-15x=20-44$

  $7x=24$

  $x=\frac{24}{7}$

Therefore the value of x is $\frac{24}{7}$

      $2x=2*\frac{24}{7} = \frac{48}{7}$

      $3x=3*\frac{24}{7} = \frac{72}{7}$

                 Hope it helps you^_^