Question

ABCD is a rectangle if AB = 15 cm and AD = 8 cm then find AC.

Answer 1

Answer:

AB=x=CD,

AD=y=BC,

AC=z

By Pythagoras theorem

z

2

=x

2

+y

2

-------(1)

Given

AC+AB=5AD

2+x=5y

z=5y−x -------(2)

squaring on both sides

z

2

=25y

2

+x

2

−10xy --------(3)

subtract equation (1) from (3)

we get z

2

=25y

2

+x

2

−10xy

−z

2

=−y

2

−x

2

−0

24y

2

−10xy=0

y

x

=

5

12

AC−AD=8

z−y=8

z=8+5

z=13

Area =12×5=60sq.units

Answer 2

Answer:

AB^2 + AD^2 = AC^2

15^2 + 8^2 =AC^2

225 + 64 = AC^2

289 = AC^2

AC = 17