The three sides of a triangle are 15, 25 and x units. Which one of the following is correct?

We know that in any triangle
"the sum of two sides is always greater than its third side" and
"the difference of two sides is always less than its third side".
(i) 2 + 3 is not greater than 5
(ii) |5 - 2| not less than 3

Area of rhombus = (d₁ x d₂) / 2
? (d x 2d ) / 2 = 144
? d² = 144
? d = 12
? Length of diagonal = 12 cm, 24 cm

Let length of the longer diagonal = d cm
Then, length of other diagonal = 0.8 x d cm
Area of rhombus = (1/2) x d x 0.8 x d = 2/5 d²
= 2/5 d²

Area of square of the length of the longer diagonal = d²

So the area of the rhombus is 2/5 times the square of the length of the longer diagonal.

Area of parallelogram = Side of parallelogram x distance from the opposite side
= 14 x 16 cm²
= 224 cm²

AB = 6 cm ; AD = 4 cm and ? BAD = 30°
Area of parallelogram ABCD = AB x AD x sin 30°
= 6 x 4 x sin 30° = 12 cm²

According to the question,
?3a²/4 = 3?3 [ side = a, and area = ?3a²/4]
? a²/4 = 3
? a² = 3 x 4
? a = 2?3

? Required perimeter = 3a
=3 x 2?3
= 6?3 cm

Given ratio = 1/3 : 1/4 : 1/5 = 20 : 15 : 12
Let length of the sides be 20k, 15k and 12k.

Then, according to the question,
20k + 15k + 12k = 94
? 47k = 94
? k = 94/47 = 2

Smallest side = 12k = 12 x 2 = 24 cm

Given that, perimeter = 90 cm
? 3a = 90 cm       [a = side]
? a = 90/3 = 30 cm
? Area = ?3a² / 4 = ?3/4 x (30)²
= 900 x ?3/4 = 225?3 sq cm

According to the question,
area = ?3a²/4
= ?243 /4
? a² = ?81 x 3/?3
? a = ?9
= 3 cm

Diagonal of square = ?2a [a = side]
4?2 = ?2 a
a = 4 cm
Now, area of square = a² = (4²) = 16
Side of a square whose area is 2 x 16.
a₁² = 32
? a₁ = ?32 ?a₁4?2

Now, diagonal of new square = ?2a
= ?2x 4 ?2
= 8 cm