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Viefleur [7K]
3 years ago
5

Please help!! ABCD is a square. If AC = 26, Find BC a. 7 b. 26 c. 12 d. 18.4

Mathematics
2 answers:
myrzilka [38]3 years ago
7 0
Since this is a square and we have the diagonal, we can use the formula Square root of 2 times d/2 where the diagonal is d, we can find the side (sqrt 2 * d/2)
sqrt 2 * 26/2 = 18.38. Rounding our decimal we get 18.4, so the answer is d. Hope this helps
blsea [12.9K]3 years ago
3 0
<h3>Given :-</h3>
  • the shape is a Square
  • AC = 26.

\\  \\

<h3>To find:-</h3>
  • BC

\\  \\

<h3>Solution:-</h3>

<u>Let</u><u> </u><u>AC</u><u> </u><u>=</u><u> </u><u>x</u>.

\\

As given figureis square, therefore all sides are equal :-

  • AB = x
  • AD = x
  • DC = x

\\

So now instead of square focus on triangle ABC.

where :-

\small \rm \angle B = 90 \degree

\\

<u>Equation formed:-</u>

\\  \\

\rm \dashrightarrow AC {}^{2}  = AB {}^{2}  + BC {}^{2}

\\

\rm \dashrightarrow 26 {}^{2}  = x{}^{2}  + x {}^{2}

\\

\rm \dashrightarrow 26 {}^{2}  =2x {}^{2}

\\

\rm \dashrightarrow 26 \times 26 =2x {}^{2}

\\

\rm \dashrightarrow2x {}^{2}  =  26 \times 26

\\  \\

\rm \dashrightarrow x {}^{2}=\dfrac{ 26 \times 26 }{2}

\\  \\

\rm \dashrightarrow x {}^{2}=\dfrac{ 26 \times \cancel{26 }}{\cancel{2}}

\\  \\

\rm \dashrightarrow x {}^{2}=\dfrac{ 26 \times 13}{1}

\\  \\

\rm \dashrightarrow x {}^{2}=26 \times 13

\\

\rm \dashrightarrow x = \sqrt{26 \times 13}

\\

\rm \dashrightarrow x = \sqrt{338}

\\

\bf \dashrightarrow x = 18.38

\\ \\

Formula used:-

\bigstar \boxed{\tt Hypotenuse^2 = Base^2+Perpendicular^2}

\\ \\

Therefore BC is equal to <u>18.38</u><u> </u><u>cm</u><u>.</u>

<h2>____________________</h2>

⭑Related Concept⭑

Property of square:-

  • All sides of square are equal.

  • All angles of square are equal.

  • All angles of square are in 90°.

  • The diagonals of a square bisect each other and meet at 90°.

  • There are four sides and four angles in square.

  • Opposite sides of a square are parallel to each other.
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