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Elza [17]
3 years ago
13

8/x=4/x+10 What's this proportion

Mathematics
1 answer:
user100 [1]3 years ago
6 0
2 ways:
1. solve for x
2. simplify the 10 so it can add to the 4/x

if you use 1. solve for x

8/x=4/x+10
subtract 4/x from both sides
4/x=10
multiply both sides by x
4=10x
divide both side sby 10
0.4=x

proportion is 8/0.4=4/0.4+10


if you use 2. make 10 addable to 4/x

4/x+10/1
multiply 10/1 by x/x
4/x+10x/x=(4+10x)/x
8/x=(4+10x)/x
multiply both sides by x to clear fraciton
8=4+10x
subtract 4
4=10x
divide 10
0.4=x
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<h3>Need to FinD :</h3>

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\red{\frak{Given}} \begin{cases} & \sf{The\ measure\ of\ one\ angle\ of\ traingle\ is\ {\pmb{\sf{10^{\circ}}}}.} \\ & \sf{The\ other\ two\ angles\ are\ in\ the\ ratio\ of\ {\pmb{\sf{3\ :\ 14}}}.} \end{cases}

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Angle sum property,

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\rule{200}{3}

\sf \dashrightarrow {10^{\circ}\ +\ 3x\ +\ 14x\ =\ 180^{\circ}} \\ \\ \\ \sf \dashrightarrow {10^{\circ}\ +\ 17x\ =\ 180^{\circ}} \\ \\ \\ \sf \dashrightarrow {17x\ =\ 180^{\circ}\ -\ 10^{\circ}} \\ \\ \\ \sf \dashrightarrow {17x\ =\ 170^{\circ}} \\ \\ \\ \sf \dashrightarrow {x\ =\ \dfrac{\cancel{170^{\circ}}}{\cancel{17}}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{x\ =\ 10^{\circ}.}}}}_{\sf \blue {\tiny{Value\ of\ x}}}}

∴ Hence, the value of x is 10°. Now, let us find out the other two angles of the triangle.

\rule{200}{3}

Second AnglE :

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∴ Hence, the measure of the second angle of triangle is 30°. Now, let us find out the third angle of triangle.

\rule{200}{3}

Third AnglE :

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  • 14 × 10
  • 140°

∴ Hence, the measure of the third angle of the triangle is 140°.

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