Question

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

Answer 1

Answer:

The length of Diagonal BD is 48 cm.

Step-by-step explanation:

Given:

The perimeter of the rhombus = 100 cm

Length of the diagonal AC(Diagonal d1) = 14 cm

Length of the diagonal BD(Diagonal d2) we have to find.

=>  $\sqrt{d1^{2} } +d2^{2} \\\\= 100=2\sqrt{196} + d2^{2} \\\\Simplifying further we get:\\\\= 50 = \sqrt{196}+d2^{2} \\\\= 2500 = 196 + d2^{2} \\\\= d2 = \sqrt{2500} -196\\\\=\sqrt{2304}$

= 48 cm

Therefore, the length of Diagonal BD is 48 cm.

Answer 2

SOLUTION:-

Given:

•The perimeter of rhombus ABCD is 100cm.

•If the length of the diagonal AC is 14cm.

To find:

The length of the diagonal BD.

Explanation:

We have,

Perimeter= 100cm

We know that, formula of the perimeter of rhombus;

$= > 2 \sqrt{ {d1}^{2} + {d2}^{2} }$

So,

•Length of first diagonal (d1)= 14cm.

$= > 2\sqrt{ {14}^{2} + {d2}^{2} } = 100 \\ \\ = > \sqrt{196 + {d2}^{2} } = \frac{100}{2} \\ \\ = > \sqrt{196 + {d2}^{2} } = 50 \\ \\ = > 196 + {d2}^{2} = {50}^{2} \\ \\ = > 196 + {d2}^{2} = 2500 \\ \\ = > {d2}^{2} = 2500 - 196 \\ \\ = > {d2}^{2} = 2304 \\ \\ = > d2 = \sqrt{2304} \\ \\ = > d2 = 48cm$

Thus,

The length of diagonal BD is 48cm.

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