Question

Vertices of the smaller square divide the edges of larger square in a 3:2 ratio. If is the irreducible fraction of the area of smaller square to that of the bigger square, what is q - p?​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:  is q - p $= 12$

Explanation:

• Area, ratio, Pythagorean theorem.

• First, we need the measure of the sides.

• We know,  $2:3=2x:3x$ for $x > 0$

         According to the ratio $(x > 0)$

       The shorter side of a triangle is $2x$

       The longer side of a triangle is  $3x$

• Then, find the hypotenuse.

          $(Base)^{2} +( perpendicular)^{2} =( hypotenuse)^{2}$

[This is the Pythagorean theorem. Here we are given the length of the   base and perpendicular.]

         ⇒ $(2x)^{2} +(3x)^{2} =(hypotenuse )^{2}$

        ⇒ $4x^{2} +9x^{2} = (hypotenuse)^{2}$

        ⇒ $(hypotenuse) =\sqrt{3x}$

• As we found its side lengths, the area of the smaller square is $13x^{2}$

• The area of a larger square is $25x^{2}$

                $\frac{(Area)(smaller square)}{(Area)(Bigger square)} =\frac{13}{25}$

• We get $q-p =25-13$

                              $=12$