Question

answer in detail with steps

Answer 1

Question:

The perimeter of a rhombus is 100 cm and one of its diagonals is 40 cm long. Find the length of the other diagonal.

Answer:

The length of the other diagonal of rhombus is 30 cm.

Step-by-step-explanation:

We have given that, perimeter of rhombus is 100 cm and its one diagonal is 40 cm.

We have to find, the length of other diagonal of the rhombus.

We know that,

$\sf\:Perimeter\:of\:rhombus\:with\:diagonals\:=\:2\:\sqrt{d^{2}_{1}\:+\:d^{2}_{2}}\\\\\implies\sf\:100\:=\:2\:\sqrt{(\:40\:)^{2}\:+\:d^{2}_{2}}\\\\\implies\sf\:\cancel{\frac{100}{2}}\:=\:\sqrt{1600\:+\:d^{2}_{2}}\\\\\implies\sf\:50\:=\:\sqrt{1600\:+\:d^{2}_{2}}\\\\\implies\sf\:(\:50\:)^{2}\:=\:\cancel{\sqrt{1600\:+\:d^{2}_{2}}}^{\cancel2}\:\:\:\:-\:-\:-\:[\:Taking\:square\:of\:both\:sides\:]\\\\\implies\sf\:2500\:=\:1600\:+\:d^{2}_{2}\\\\\implies\sf\:2500\:-\:1600\:=\:d^{2}_{2}\\\\\implies\sf\:d^{2}_{2}\:=\:900\\\\\implies\sf\:d_{2}\:=\:\pm\:30\:\:\:-\:-\:-\:[\:Taking\:square\:root\:of\:both\:sides\:]\\\\\implies\boxed{\red{\sf\:d_{2}\:=\:30\:cm}}\:\:\:[\sf\:\because\:Length\:cannot\:be\:negative\:]$

Additional Information:

1. Rhombus:

A quadrilateral having all sides congruent is called as rhombus.

2. Properties of rhombus:

1. Opposite sides are of equal measures.

2. Opposite angles are congruent.

3. Diagonals bisect each other.

4. Diagonals of rhombus are perpendicular bisectors of each other i.e. at 90°.