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Find the value of π§ in the following parallelogram.
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The diagram shows a quadrilateral, which weβre told is a parallelogram.
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Its diagonals have also been drawn in.
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The diagonals intersect at a point in the interior of the parallelogram.
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The two parts of one of the diagonals have been given as expressions in terms of the variable π§, whose value weβre looking to calculate.
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In order to answer this question, we need to think about what we know about the diagonals of parallelograms.
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An important key fact is this the diagonals of a parallelogram bisect each other.
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What does this mean well?
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The word βbisectβ means to cut in half.
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So the two portions of each diagonal are the same length.
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So for the diagonal whose lengths have been given in terms of the variable π§, this means that the two expressions must be equal to each other.
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We can express this as an equation six π§ minus five is equal to π§ plus 10.
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The problem has now become an algebraic one.
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In order to find the value of π§, we need to solve this equation.
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First Iβm going to add five to both sides of the equation.
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This gives six π§ is equal to π§ plus 15.
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Now there are terms involving π§ on both sides of the equation.
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So next, Iβd like to subtract π§ from both sides.
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Subtracting π§ from the left-hand side gives five π§.
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And subtracting π§ from the right-hand side gives 15.
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So now we have five π§ is equal to 15.
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The final step in solving this equation is to divide both sides by five.
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This gives the solution to the problem: the value of π§ is three.