Question

Q.6 A triangle has sides 25. 39. 34 units. If the area of a square exceeds the area of this triangle by 21 units, then the side of
the square is:​

Answer 1

Answer:

SOLUTION

Given:

Sides of triangle are 25, 39 and 34 units.

Area of square is more than that of triangle = 21 units

Formula:

Area of triangle = √[s (s – a) (s – b) (s – c)]

s = (a + b + c)/2

Perimeter of the triangle = a + b + c

Calculation:

a = 25, b = 39 and c = 34

S = (25 + 39 + 34)/2

⇒ S = 98/2 = 49 unit

Area of triangle ⇒

⇒ √[49 (49 – 25) (49 – 39) (49 – 34)

⇒ √[49 × 24 × 10 × 15]

⇒ √(7 × 7 × 2 × 2 × 2 × 3 × 2 × 5 × 3 × 5)

⇒ 7 × 2 × 2 × 3 × 5

⇒ 420

Area of square = 420 + 21 = 441

∴ Side of square = √441 = 21 unit

Answer 2

Answer:

SOLUTION

Given:

Sides of triangle are 25, 39 and 34 units.

Area of square is more than that of triangle = 21 units

Formula:

Area of triangle = √[s (s – a) (s – b) (s – c)]

s = (a + b + c)/2

Perimeter of the triangle = a + b + c

Calculation:

a = 25, b = 39 and c = 34

S = (25 + 39 + 34)/2

⇒ S = 98/2 = 49 unit

Area of triangle ⇒

⇒ √[49 (49 – 25) (49 – 39) (49 – 34)

⇒ √[49 × 24 × 10 × 15]

⇒ √(7 × 7 × 2 × 2 × 2 × 3 × 2 × 5 × 3 × 5)

⇒ 7 × 2 × 2 × 3 × 5

⇒ 420

Area of square = 420 + 21 = 441

∴ Side of square = √441 = 21 unit