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uysha [10]
3 years ago
6

ABCD rhombus, AC:BD = 4:3 Perimeter ABCD = 20 cm Find: Area of ABCD

Mathematics
1 answer:
AlladinOne [14]3 years ago
6 0
Given that the perimeter of rhombus ABCD is 20 cm, the length of the sides will be:
length=20/4=5 cm
the ratio of the diagonals is 4:3, hence suppose the common factor on the diagonals is x such that:
AC=4x and BD=3x
using Pythagorean theorem, the length of one side of the rhombus will be:
c^2=a^2+b^2
substituting our values we get:
5²=(2x)²+(1.5x)²
25=4x²+2.25x²
25=6.25x²
x²=4
x=2
hence the length of the diagonals will be:
AC=4x=4×2=8 cm
BD=3x=3×2=6 cm
Hence the area of the rhombus wll be:
Area=1/2(AC×BD)
=1/2×8×6
=24 cm²
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Hello macelynn190!

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

\huge \tt \frac{5 - 2(a + 3b)}{2}

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

To solve this question we need to substitute the given values of 'a' & 'b' in the equation & then simplify it.

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