Question

ABCD is a kite, so start overline, A, C, end overline

AC is perpendicular to⊥ start overline, D, B, end overline
DB and D, E, equals, E, BDE=EB. Calculate the length of start overline, A, C, end overline
AC , to the nearest tenth of a centimeter.
PLEEAAASEEE HELP

Answer 1

• 8.7cm

Solution :

In order to find the measure of segment AC, we firstly will find the measure of segment AC and then segment CE and then add them up which would give us the length of segment AC.

In order to find the length of segment AE, we are required to know that ΔADE is a right angle triangle which means one of it's angle is 90° and thus, either of it's side can be found using Pythagoras theorem .

Here , we have AD = 5cm and DE = 8/2cm( DE = EB and DE + EB = DB which gives us each of them measuring 4cm)

So ,we can find AE now,

• Pythagoras theorem states that the square of the hypotenuse is equal to the square of the base and the perpendicular of the triangle.

i.e.

• H = √(P^2 + B^2)

wherein,

• H = hypotenuse (here, 5cm)
• P = perpendicular (here,AE)
• B = base (here,1cm)

Thus,

• 5cm = √((AE)^2 + (4cm)^2)
• AE = √((5cm)^2 - (4cm)^2)
• AE = √(25cm^2 - 16cm^2)
• AE = √(9cm^2)
• AE = 3cm

Thus, AE = 3cm

Now,

In ΔCDE,

• DE = 4cm
• CD = 7cm

Thus,

• CE = √((CD)^2 - (DE)^2)
• CE = √((7cm)^2 - (4cm)^2)
• CE = √49cm^2 - 16cm^2)
• CE = √(33cm^2)
• CE = 5.7cm

Thus, CE = 5.7cm

Since AC = CE + AE

Hence,

• AC = 5.7cm + 3cm
• AC =8.7cm

Therefore, AC = 8.7cm