Question

the perimeter of rhombus ABCD is 100cm. if the length of diagonal AC is 14 cm, find the length of diagonal BD​

Answer 1

$\bf {\huge {\underline {\boxed {\sf\purple{Answer:48\:cm}}}}}$

$\huge\sf\green {Given:}$

• Permineter of rhombus ABCD is 100 cm.

• Diagonal AC is 14 cm.

$\huge\sf\green {To\:Find :}$

• Diagonal BD

$\huge\sf\green {Solution :}$

As we know,

Perimeter of rhombus = 2 $\sqrt {(d_1)^2 + (d_2)^2}$

Now,

Put the given values in the formula.

we get,

2 $\sqrt{(14)^2+ (d_2)^2}$ = 100

➡ $\sqrt{196 + (d_2)^2}$ =$\dfrac{100}{2}$

➡ $196 + (d_2)^2$ = $(50)^2$

➡$196 + (d_2)^2$ = 2500

➡ ${d_2}^2$ = 2500 - 196

➡ ${d_2}^2$ = 2304

➡ ${d_2}$ = $\sqrt {2304}$

➡ ${d_2}$ = 48 cm

Answer: length of Diagonal BD is 48 cm.

$\huge\mathscr\red {Be\: Brainly!!!}$

Answer 2

Answer:

The length of Diagonal BD is 48 cm.

Step-by-step explanation:

Given :

• Permineter of rhombus ABCD is 100 cm.
• The length of the Diagonal AC is 14 cm.
• The length of diagonal BD​ = ?

To Find :

The length of diagonal BD​.

Solution :

We know that :

$\bigstar\;\boxed{\textsf{Perimeter of rhombus} = \sf 2 \sqrt {(d_1)^2 + (d_2)^2}}}$

Values in the equation,

$\sf\\ \\\implies 2 \sqrt{(14)^2+ (d_2)^2} = 100\\ \\ \\ \implies \sqrt{196 + (d_2)^2} =\dfrac{100}{2}\\ \\ \\\implies 196 + (d_2)^2 = (50)^2 \\ \\ \\\implies 196 + (d_2)^2 = 2500\\ \\ \\ \implies {d_2}^2 = 2500 - 196\\ \\ \\\implies {d_2}^2 = 2304\\ \\ \\\implies {d_2} = \sqrt {2304}\\ \\ \\ \implies \bf {d_2} = 48 cm$

∴ The length of Diagonal BD is 48 cm.