Question

If the diagonals of a rhombus are of length 24 & 32 cm, find the altitude of the rhombus.

Answer 1

Answer:

19.2cm=h

Step-by-step explanation:

Let ABCD be a rhombus with AC and BD as its diagonals.

We know that the diagonals of a rhombus bisect each other at right angles.

Let O be the intersecting point of both the diagonals.

Let AC=24cm and BD=32cm

OA=AC/2

OA= 24/2=12cm

OB=BD/2

OB=32/2=16cm

In rt.ΔAOB by Pythagoras theorem we have

AB²=OA²+OB²

=(12)²+(16)²

=144+256

=400

AB=20cm

Hence, each side of the rhombus is of length 20cm

Area of rhombus=1/2*AC*BD

=1/2*24*32

=12*32

Area of rhombus=base*altitude

12*32=20*h

19.2cm=h

HOPE IT HELPS!!!!!!!!

Answer 2

Hello Carousel!

$\huge \boxed{\mathfrak{Question} \downarrow}$

If the diagonals of a rhombus are of length 24 & 32 cm, find the altitude of the rhombus.

a) 15.8 cm

b) 14.2 cm

c) 12 cm

d) 19.2 cm

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

Please refer to the attached picture for the answers with steps included.

NOTE :-

• The sides of a rhombus are equal to each other.
• The point of intersection of the diagonals (marked as O in the figure) forms 90° angles (which is why we used the pythagoras property to solve the question).
• Since 0 is the point of intersection, it's also the midpoint of the diagonals. (So, BO = ½ × BD & AO = ½ AC -- we used this to solve the question).

__________________

Hope it'll help you!

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