Question

Find the area of a rhombus if the the sum of the diagonal is 24 metre and the ratio of the diagonal is 3:5

Answer 1

Answer:

67.5

Step-by-step explanation:

area of rhombus = the product of the two diagonals/ 2

= let the sun of the two diagonals be x

3x+5x = 24

8x=24

x=3

1st diagonal =3*3=9

2nd = 15

area=9*45/2

=67.5

hope it helps

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Answer 2

$\huge{\tt{\underline{\underline{AnSwEr}}}}$

$\large{\sf{\underline{\underline{StEp-By-SteP -explanation}}}}$

Let the diagnols be 3x and 5x ;

Sum of diagnols = 24m

So;

$\large\implies\tt\ 3x \: + \: 5x \: = \: 24 \\ \\ \large\implies\tt\ 8x \: = \: 24 \\ \\ \large\implies\tt\ x \: = \: \frac{24}{8} \: = \: 3$

Now;

$\rule{300}{2}$

$\large{\boxed{\boxed{\sf{\red{ Area \: of \: Rhombus \: = \: \frac{1}{2} \times\ d_1 \times\ d_2}}}}}$

Accordingly put the values ;

$\large\implies\tt\frac{1}{2} \times\ 3x \times\ 5x \\ \\ \large\implies\tt\frac{1}{2} \times\ 15x^2 \\ \\ \large\implies\tt\frac{1}{2} \times\ 15 \times\ 9 \\ \\ \large\implies\tt\frac{135}{2} \: = \: 67.5$

$\rule{300}{2}$

$\sf\pink{\therefore\ Area\: of \: Rhombus \: = \: 67.5m^2}$