Raymm20idn
Answered

IDNLearn.com makes it easy to find the right answers to your questions. Discover the information you need quickly and easily with our reliable and thorough Q&A platform.

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
WindyMintidn

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.
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Find clear and concise answers at IDNLearn.com. Thanks for stopping by, and come back for more dependable solutions.