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

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

AB=X=CD,

AD=y=BC,

AC=z

By PYTHAGORAS theorem

-------(1)

Given

AC+AB=5AD

2+x=5y

z=5y−x -------(2)

SQUARING on both sides

=25y

−10xy --------(3)

subtract equation (1) from (3)

we get z

=25y

−10xy

−z

=−y

−x

−0

24y

−10xy=0

AC−AD=8

z−y=8

z=8+5

z=13

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