Question

d1 and d2 are 5:12 and perimeter of rhombus are 104 find its area

Answer 1

Let the diagonal be 5x,12x
perimeter of rhombus=2(d1+d2)
104=2 x (5x+12x)
104/2=17x
52=17x
x=3.058
d1=5 x 3.058=15.29
d2= 12 x 3.058= 36.70
Area of rhombus= d1 x d2/2= 561.38/2=280.69 sq units..

Answer 2

$\Huge{\boxed{\pink{\mathbb{QUESTION}}}}$

$D_{1}\:and\:D_{2}$ of a rhombus are in the ratio of 5:12 and the perimeter of the rhombus is 104 units. Find the area.

$\Huge{\boxed{\pink{\mathbb{ANSWER}}}}$

$\bold{Given\:that,}$

Ratio of diagonals = 5:12

Perimeter = 104 units

$\bold{To\:find,}$

Area of the rhombus = ?

Before finding the area, we have to find the value of each diagonal. For this,

$\bold{We\:know\:that,}$

Perimeter = $2(D_{1}+D_{2})$

Let x be the diagonals,

Then, 104 units = 2(5x+12x)

104 units = 10x+24x

104 units = 34x

x = $\frac{104}{34}$

x = 3.05 (approximately)

$\bold{[By\:substituting\:the\:value\:of\:x,]}$

$D_{1} = 5x = 5 \times 3.05 = 15.25\:units$

$D_{2} = 12x = 12 \times 3.05 = 36.6\:units$

$\textit{Now\:we'll\:find\:the\:area.}$

$\bold{We\:know\:that,}$

Area of a rhombus = $\frac{D_{1} \times D_{2}}{2}$

Area of rhombus = $\frac{15.25 \times 36.6}{2}$

Area of rhombus = $\frac{558.15}{2}$

Area of rhombus ≈ 279.05 squared units

$\Huge{\boxed{\pink{\mathbb{NOTE}}}}$

If unit is not given in the question, then you should write it has 'units'. Should not leave it, otherwise, your marks will be cut.