Parallelogram ABCD is a rectangle whose diagonals are AC and BD. If AC=10x-7 and...

$\huge{ \mathcal {PROBLEM}}$

Parallelogram ABCD is a rectangle whose diagonals are AC and BD. If AC = 10x - 7 and BD = 5x + 3, what is the value of x?

$\huge{ \mathcal {SOLVING}}$

$\sf AC≅BD \\ \tt 10x - 7 = 5x + 3 \: \: \: \: \\ \tt 10x - 5x = 3 + 7 \: \: \: \: \: \: \: \: \: \\ \tt \frac{ \cancel5x}{ \cancel5} = \frac{10}{5} \: \: \\ \boxed{ \tt{ \: x = 2 \: }} \: \:$

$\huge{ \mathcal {ANSWER}}$

Parallelogram ABCD is a rectangle whose diagonals are AC and BD. If AC = 10x - 7 and BD = 5x + 3, what is the value of x?

$\huge{ \underline{ \boxed{ \tt{x = 2}}}}$

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${\tt{Question : }}$

Parallelogram ABCD is a rectangle whose diagonals are AC and BD. If AC=10x-7 and BD=5x+3, what is the value of x?

${\tt{Solving : }} \\ {\tt{AC≅BD}}\\{\tt{10x - 7 = 5x + 3}} \\{\tt{10x - 7x - 7 = 3}} \\{\tt{10x - 5x = 3 + 7}} \\ {\tt{5x = 3 + 7}} \\{\tt{5x = 10}} \\{\tt{10 \div 5}} \\{\tt{x = \boxed{\tt{2}}}}$

Answer :

${\tt{the \: value \: of \: x \: is \boxed{\tt{2}}}}$

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$\sf AC≅BD \\ \tt 10x - 7 = 5x + 3 \: \: \: \: \\ \tt 10x - 5x = 3 + 7 \: \: \: \: \: \: \: \: \: \\ \tt \frac{ \cancel5x}{ \cancel5} = \frac{10}{5} \: \: \\ \boxed{ \tt{ \: x = 2 \: }} \: \:$

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