If AB and AC, inscribed in a square as shown above, are each

Question

If AB and AC, inscribed in a square as shown above, are each 10 centimeters in length, what is the area of the square (in centimeters)?

(A) 40sqrt3
(B) 74
(C) 80
(D) 50sqrt2
(E) 100

mbagal1 · Answer

Let the length of the side of the square be l.

100 = (l^2 + (l/2)^2 ) 
5/4* l^2 = 100

l^2 = 400/5 = 80

800_gal · Answer

Agree with 80. 
Let the sides of the square be 2x, therefore the area of the square is 4x^2.
If we drop a perpendicular from the vertex of the triangle it would intersect the base of the triangle making two rt angled triangle with bases x and perpendicular sides 2x, and hypotenuse 10.
Now we can write 
sqrt((2x)^2 + x^2) = 10
or, ((2x)^2 + x^2) = 100
or, 5x^2 = 100
or, x^2 = 20
therefore 4x^2= 80

yogeshsheth · Answer

Can someone kindly explain why A is considered to be the midpoint?

ncp · Answer

An isoscleled triangle with base as the side of a square can be formed only if the vertex of the triangle is the midpoint of the opposite side of the square. 

Draw an isosceles triangle and try moving the vertex away from the mid-point of the side of the square. You will see that the 2 sides of the triangle will become unequal.

MBAlad · Answer

Side = x = side of square
Other side (of triangle) = x/2
Hyp = 10

x^2 + (x/2)^2 = 100 -----> x^2 + x^2/4 = 100

4x^2/4 + x^2/4 = 100 ------> 4x^2 + x^2 = 400

5x^2 = 400 -----> x^2 = 80

If AB and AC, inscribed in a square as shown above, are each

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