Question

. Find the perimeter of a quadrilateral whose all sides are equal and diagonals are 24 cm and 10 cm respectively

Answer 1

Answer:

Perimeter = 52cm

Step-by-step explanation:

Hello!

A quadrilateral whose all sides are equal can either be a square or a rhombus. But it is given that the diagonals are unequal, hence the quadrilateral has to be a rhombus.

Here's the formula for finding the side of the rhombus if diagonals are given:

$side = \sqrt{{( \frac{ digonal \: 1}{2})} ^{2} + {( \frac{ digonal \: 2}{2})} ^{2}}$

Diagonal 1 = 24cm

Diagonal 2 = 10cm

Substituting,

$side = \sqrt{{( \frac{ 24}{2})} ^{2} + {( \frac{ 10}{2})} ^{2}} = \sqrt{ {12}^{2} + {5}^{2} } = \sqrt{169} = 13$

Hence, the side of the rhombus = 13cm

Perimeter of a rhombus = 4 × side = 4 × 13 = 52cm.

(If you want a detailed explanation of how I arrived at the formula, please check my other answer which is just below this one you see in my Profile >> Answers >> Maths.)

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