The ratio of the area of square of side a and equilateral triangle of side a is?

Original area = ?(d/2)²
= (?d²) / 4

New area = ?(2d/2)²
= ?d²

Increase in area = (?d² - ?d²/4)
= 3?d²/4

? Required increase percent
= [(3?d²)/4 x 4/(?d²) x 100]%
= 300%

Let the diagonal of one square be (2d) cm
Then, diagonal of another square = d cm

? Area of first square = [ 1/2 x (2d)²] cm²
Area of second square = (1/2 x d²) cm²

? Ratio of area = (2d)²/ d²
= 4/1 = 4: 1

Length of the longest pole = ? [(10)² + (8)²] m
= ? 164 m
= 12.8 m

Let breadth = b, length = 2b
? Area of rectangle = 2b x b
= 2b²

As per question.
? (2b - 5 ) (b + 5 ) = 2b² + 75
? 5b = 75 + 25
? 5b = 100
? b = 100 / 5 = 20

Hence, length of the rectangle =2b
= 2 x 20
= 40 cm.

Area = 1/2 x (Diagonal)²
= (1/2) x 5.2 x 5.2 cm²
= 13.52 cm²

Area of equilateral triangle = ?3/4 a² = 4?3.
? a² = 16
? a = 4 cm

Req. Area = ?3/4 x a² = ?3/4 x 8² cm²
= 16?3 cm²

Given that, a = 8 cm, b = 10 cm and c = 12 cm

We know, that
s = (a + b + c)/2
= (8 + 10 + 12)/2
= 30/2 = 15 cm

? (s - a) = (15 - 8) = 7 cm
(s - b) = (15 - 10) = 5 cm
(s - c) = (15 - 12) = 3 cm

? Area = ?s(s - a) (s - b) (s - c)
= ?15 x 7 x 5 x 3
= ?1575
= ?25 x 63
= 5?63 cm

Given that, a = 6 cm, b = 4 cm and c = 5 cm
Required perimeter = a + b + c
= 6 + 4 + 5 cm
= 15 cm

Given that,
area = 40 sq cm,
base = 28 cm and
height = perpendicular = ?

Area = (base x perpendicular) / 2
? 40 = (28 x perpendicular) / 2
? perpendicular = 40/14 = 20/7
= 2⁶/₇ cm