Question

The length of rectangular painting is 7 inches long than its width. If the diagonal is 13inches, what are the dimensions of the painting?

Answer 1

Step-by-step explanation:

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$\bf \huge \: \: QUESTION \: \: \:$

• The length of rectangular painting is 7 inches long than its width. If the diagonal is 13inches, what are the dimensions of the painting?

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$\bf \huge \: \: GIVEN \: \: \:$

• The length of rectangular painting is 7 inches long than its width.
• If the diagonal is 13inches,

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$\bf \huge \: \: To \: Find \: \:$

• what are the dimensions of the painting?

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The diagonal is the hypotenuse of a rectangular triangle.

Then:-

$\bf \:d^2=l^2+w^2 \:$

( we know)

$\bf \:13^2=169 \:$

$\bf \:=(x+7)^2+x^2 \:$

$\bf \:=x^2+14x+49+x^2 \:$

$\bf \:->2x^2+14x-120=0 \:$

$\bf \:->x^2+7x-60=0 \:$

A simple quadratic equation :-

$\bf \:(x+12)(x-5)=0 \:$

$\bf \:-> x=-12 or x=5 \:$

Answer is 5 Becouse x = -12 cm not imposible ..