Question

if the area of the rhombus is 96 cm² and the one diagonal is 4 cm longer than the other, find the two diagonals​

Answer 1

Given :-

• Area of rhombus = 96 cm²
• One diagonal = 4 cm + other diagonal

To find :-

• Two diagonals = ?

Solution :-

Here, let one diagonal be y cm & other diagonal be (y + 4) cm

As we know,

→ Area of rhombus = ½ × d1 × d2

Putting all values

→ 96 cm² = ½ × (y + 4) × y

→ 96 cm² = { y(y + 4) }/2

→ 96 × 2 = y² + 4y

→ 192 = y² + 4y

→ y² + 4y - 192 = 0

→ y² + 16y - 12y - 192 = 0

→ y (y + 16) - 12(y + 16) = 0

→ (y - 12)(y + 16) = 0

→ y = 12 or y = -16

∵ Diagonal of rhombus can't be negative

∴ y = 12 cm

So, one diagonal of rhombus is 12 cm

Finding another diagonal

→ Other diagonal = y + 4

→ Other diagonal = 12 + 4

→ Other diagonal = 16 cm

Therefore,

Two diagonals of rhombus are 16 cm & 12 cm respectively.

Answer 2

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QUESTION :

if the area of the rhombus is 96 cm² and the one diagonal is 4 cm longer than the other, find the two diagonals.

SOLUTION :

We know that area of a Rhombus is equal to 1/2 × d1 × d2

Let the length of Diagonal 1 be X cm .

Therefore the length of the other diagonal is X + 4 cm .

=> Area = 1/2 × X × X + 4 = 96

=> X( x + 4 ) = 192

=> X^2 + 4X - 192 = 0

=> X^2 + 16 X -12 X - 192 = 0

=> X ( X + 16 ) - 12 ( X + 16 ) = 0

=> ( X - 12 ) ( X + 16 ) = 0

=> X = 12 cm .

=> Diagonal 1 is 12 cm .

=> Diagonal 2 = X + 4 = 16 cm.

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A n S w E r -

The lengths of the two diagonals are 12 cm and 16 cm respectively..