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3 years ago

15

Mathematics

1 answer:

Evgesh-ka [11]3 years ago

8 0

Answer:

Height = 14.4

Step-by-step explanation:

The diagonals meet at right angles. Interesting property.

The hypotenuse is the side of the rhombus = 15 cm

One of the sides of the small triangles created by the intersection of the diagonals = 24/2 = 12

You can find the other side of the the triangle by using the Pythagorean Theorem

a^2 + b^2 = c^2

c = 15

a = 12

b = ?

12^2 + b^2 = 15^2

144 + b^2 = 225

b^2 = 225 - 144

b^2 = 81

b = 9

The area of this right angle = 9 * 12/2 = 54

There are 4 of them so 4 * 54 = 216

That's the area of the rhombus.

The h= Area / b

b = 15

h = 216/15

h = 14.4

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