Question

the area of a triangle is 42 square metre find the base as the altitude exceeds the base by 8 solve the quadratic equation word problems​

Answer 1

Answer:

The base of triangle is 6 m

The height of triangle is 14 m

Step-by-step explanation:

Let,

The base of triangle = x

The height of triangle = x + 8

The area of a triangle is 42 square meter

So,

The area of a triangle = 1/2 × base × height

⇒ 1/2 × base × height = 42

⇒ 1/2 × (x) × (x +8) = 42

⇒ x² + 8x = 42 × 2

⇒ x² + 8x = 84

⇒ x² + 8x - 84 = 0

⇒ x² + 14x - 6x - 84 = 0

⇒ x (x + 14) - 6 (x + 14) = 0

⇒ (x + 14) (x - 6) = 0

⇒ x = - 14 Or x = 6

Hence,

⇒ x = 6

The base of triangle = 6 m

___________________________

★ The height of triangle = x + 8

⇒ x + 8

⇒ 6 + 8

⇒ 14

The height of triangle = 14 m

Therefore,

The base of triangle is 6 m

The height of triangle is 14 m

Answer 2

$\bf{\underline{Question:-}}$

the area of a triangle is 42 square metre find the base as the altitude exceeds the base by 8 solve the quadratic equation.

$\bf{\underline{Given:-}}$

• Area of ∆ = 42 sq.m
• Base = ?
• Altitude ( height ) = ?

Let,

• The base be = X m
• Altitude exceeds the base by 8 = x + 8 m

$\bf{\underline{</strong><strong>Formu</strong><strong>la</strong><strong>:-}}$

$\bf\large ★\: \frac{1}{2}×base × height ( altitude )$

$\bf{\underline{Solution:-}}$

$\bf → \frac{1}{2} × x × x + 8 = 42$

$\tt {\underline{\fbox{BY\: SPLITTING\:METHOD}}}$

$\bf → x^2 + 8 x = 42× 2$

$\bf → x^2 + 8x - 84 = 0$

$\bf → x^2 + ( 14 - 6)x - 84 = 0$

$\bf → x^2 + 14x - 6x - 84 = 0$

$\bf → x ( x + 14 ) - 6 ( x + 14 ) = 0$

$\bf → ( x - 6 ) ( x + 14 ) = 0$

$\bf → x - 6 = 0$

$\bf → x = 6$ either

$\bf → x + 14 = 0$

$\bf → x - 14$

• We know Distance can never be zero " 0 "

So,

we neglect - 14

• we take 6
• The base of ∆ is 6 metre
• Altitude = x + 8 = 6 + 8 = 14m

$\bf{\underline{Hence:-}}$

• The base of the ∆ is 6m
• The Height of the ∆ is 14 m