Question

if A:B:C is 2:3:4 and A²+B²+C²=11600 then find (A-B+C)
step by step explanation​

Answer 1

Step-by-step explanation:

Let ratios be Ax, Bx, and Cx.

A:B:C = 2:3:4.

Hence ratios become 2x, 3x, and 4x.

Now, we know that -

${2x}^{2} + {3x}^{2} + {4x}^{2} \: = 11600 \\ {9x}^{2} = 11600 \\ {x}^{2} = \frac{11600}{9} \\ x = \sqrt{ \frac{11600}{9} } \\ x = \frac{20}{3 } \sqrt{29}$

Substitute value of x, and find values of A, B & C -

A =

$2x = 2( \frac{20}{3} \sqrt{29} ) = \frac{40}{3} \sqrt{29}$

B =

$3x = 3( \frac{20}{3} \sqrt{29} ) = 20 \sqrt{29} = \frac{60}{3} \sqrt{29}$

C =

$4x = 4( \frac{20}{3} \sqrt{29} ) = \frac{80}{3} \sqrt{29} )$

Hence, (A - B + C)

$\frac{40}{3} \sqrt{29} - \frac{60}{3} \sqrt{29} + \frac{80}{3} \sqrt{29} = \frac{60}{3} \sqrt{29}$