raymm20
Answered

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please help!! ABCD is a square. If AC = 26, Find BC

a. 7
b. 26
c. 12
d. 18.4

Please Help ABCD Is A Square If AC 26 Find BC A 7 B 26 C 12 D 184 class=

Sagot :

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
WindyMint

Given :-

  • the shape is a Square
  • AC = 26.

[tex] \\ \\ [/tex]

To find:-

  • BC

[tex] \\ \\ [/tex]

Solution:-

Let AC = x.

[tex] \\ [/tex]

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

  • AB = x
  • AD = x
  • DC = x

[tex] \\ [/tex]

So now instead of square focus on triangle ABC.

where :-

[tex] \small \rm \angle B = 90 \degree[/tex]

[tex] \\ [/tex]

Equation formed:-

[tex] \\ \\ [/tex]

[tex] \rm \dashrightarrow AC {}^{2} = AB {}^{2} + BC {}^{2} [/tex]

[tex] \\ [/tex]

[tex] \rm \dashrightarrow 26 {}^{2} = x{}^{2} + x {}^{2} [/tex]

[tex] \\ [/tex]

[tex] \rm \dashrightarrow 26 {}^{2} =2x {}^{2} [/tex]

[tex] \\ [/tex]

[tex] \rm \dashrightarrow 26 \times 26 =2x {}^{2} [/tex]

[tex] \\ [/tex]

[tex] \rm \dashrightarrow2x {}^{2} = 26 \times 26 [/tex]

[tex] \\ \\ [/tex]

[tex] \rm \dashrightarrow x {}^{2}=\dfrac{ 26 \times 26 }{2}[/tex]

[tex] \\ \\ [/tex]

[tex] \rm \dashrightarrow x {}^{2}=\dfrac{ 26 \times \cancel{26 }}{\cancel{2}}[/tex]

[tex] \\ \\ [/tex]

[tex] \rm \dashrightarrow x {}^{2}=\dfrac{ 26 \times 13}{1}[/tex]

[tex] \\ \\ [/tex]

[tex] \rm \dashrightarrow x {}^{2}=26 \times 13[/tex]

[tex] \\ [/tex]

[tex] \rm \dashrightarrow x = \sqrt{26 \times 13} [/tex]

[tex] \\ [/tex]

[tex] \rm \dashrightarrow x = \sqrt{338} [/tex]

[tex] \\ [/tex]

[tex] \bf \dashrightarrow x = 18.38[/tex]

[tex]\\ \\ [/tex]

Formula used:-

[tex] \bigstar \boxed{\tt Hypotenuse^2 = Base^2+Perpendicular^2}[/tex]

[tex]\\ \\ [/tex]

Therefore BC is equal to 18.38 cm.

____________________

⭑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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