Question

1
1. Find a row echelon matrix which is row equivalent to
To 0 - 2 3 1
2
1 4 3
A=
and find PR (A).
1 2 -3 1 2
4 8 2 3 5
4.​

Answer 1

Given:

The Base and Height of the triangle are in the ratio of 2:3. And, area of the triangle is 180 cm².

To find:

The Base and Height of triangle.

Solution: Let the Base and Height of the triangle be 2x and 3x respectively.

As we know that,

★ Area of triangle = 1/2 × (Base) × (Height) ★

Area of the triangle is given that is 180 cm². Therefore by using the formula,

$\implies$ 108 = 1/2 × (2x) × (3x)

$\implies$ 108 = 3x²

$\implies$ x² = 108/3

$\implies$ x² = 36

$\implies$ x = √36

$\implies$ x = 6 ★

Hence,

➠ Base of the triangle, 2x = 2 × (6) = 12 cm

➠ Height of the triangle, 3x = 3 × (6) = 18 cm

Hence, Base and Height of the triangle are 12 cm and 18 cm respectively.

Answer 2

Step-by-step explanation:

Given:

The Base and Height of the triangle are in the ratio of 2:3. And, area of the triangle is 180 cm².

To find:

The Base and Height of triangle.

Solution: Let the Base and Height of the triangle be 2x and 3x respectively.

As we know that,

★ Area of triangle = 1/2 × (Base) × (Height) ★

Area of the triangle is given that is 180 cm². Therefore by using the formula,

⟹\implies⟹ 108 = 1/2 × (2x) × (3x)

⟹\implies⟹ 108 = 3x²

⟹\implies⟹ x² = 108/3

⟹\implies⟹ x² = 36

⟹\implies⟹ x = √36

⟹\implies⟹ x = 6 ★

Hence,

➠ Base of the triangle, 2x = 2 × (6) = 12 cm

➠ Height of the triangle, 3x = 3 × (6) = 18 cm

Hence, Base and Height of the triangle are 12 cm and 18 cm respectively.