Question

The perimeter of a rhombus is 60 cm and one diagonal measure 18 cm. Find the length of the other

diagonal​

Answer 1

Answer:

24 cm

Step-by-step explanation:

Given

The perimeter of the rhombus = 60 cm

We can name the rhombus ABCD

AB, BC, CD, DA are sides, and AC, BD are diagonals.

Let the side of the rhombus be 'x' cm

⇒ 4*x = 60 cm                        [∵Rhombus has 4 equal sides]

⇒ x = 60/4 = 15 cm

x = 15 cm

AB = BC = CD = AD = 15 cm

Given the length of the one diagonal AC = 18 cm

Let the length of the other diagonal be BD = 'y' cm

We know that

Diagonals of a rhombus intersect perpendicularly but the length of the diagonals is not equal.

Let us assume AD and BC intersect at O.

This forms 4 equal right-angled triangles.

Let us take one right-angled triangle Δ AOD

AO + OC = AC and AO = OC

⇒ AO = AC/2 = 18/2

∴AO = 9 cm

Similarly,

BO + OD = BD and BO = OD

⇒OD = BD/2

∴OD = y/2

ΔAOD is a right-angled triangle with side AO and OD with hypotenuse AD

By Pythagoras theorem,

In a right-angled triangle

Side² + Side² = Hypotenuse²

⇒AO² + OD² = AD²

⇒9² + (y/2)² = 15²    [Here AD is the side of rhombus]

⇒81 + (y²/4) = 225

⇒y²/4 = 225 - 81

⇒y²/4 = 144

⇒y² = 144*4

⇒y = √144*4

⇒y = 12*2

∴y = 24 cm

∴The length of the other diagonal = 24 cm