ABCD is a square. Length of one diagonal is 5cm. a) What is the length of AB
b) Find the perimeter of ABCD
c) Find the area of

Below

Step-by-step explanation:

Let D be the diagonal of this square.

D forms with AB and BC a right triangle where D is the hypotenus.

We will apply then the Pythagorian theorem

●The Pythagorian theorem

● D^2 = AB^2 + BC^2

ABCD is a square, so AB=BC

● D^2 = AB^2 + AB^2

● D^2 = 2AB^2

We khow that is D= 5 cm

● 25 = 2AB^2

● 25/2 = AB^2

● 5/√2 = AB

AB is 5√2 cm

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The perimeter is:

● P = 4AB

● P = 4×(5/√2)

● P = 20/√2

● P = 10×2/√2

● P = 10√2 cm

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The area is

● A = AB^2

● A = (5/√2)^2

● A = 25/2 cm^2

Step-by-step explanation:

the sides of a square are equal ( AB=BC=CD=DA)

diagonal of the square creates two right angle triangle

to find the side of the triangle we apply the Pythagorean theorem:

a²+b²=c² ( let AB=a, and BC=b)

2a²=25 ( since AB=BC=a)

a²=25/2

a=(5√2)/2 cm

a=3.54 ( rounded to the nearest 10)

perimeter = 4a

P=4(5√2/2)

P=10√2 cm

Area=a²=(5√2/2)²=25/2=12.5 cm^2