Question

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

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

Answer 1

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

Answer 2

Given :-

• the shape is a Square
• AC = 26.

To find:-

• BC

Solution:-

Let AC = x.

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 :-

$\small \rm \angle B = 90 \degree$

Equation formed:-

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

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

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

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

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

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

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

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

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

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

$\rm \dashrightarrow x = \sqrt{338}$

$\bf \dashrightarrow x = 18.38$

Formula used:-

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

Therefore BC is equal to 18.38 cm.

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⭑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.