IDNLearn.com offers a unique blend of expert answers and community insights. Get the information you need from our community of experts who provide accurate and comprehensive answers to all your questions.

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

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.