Math, asked by viju558, 9 months ago

The height of a triangle is 2mm less than the base if the area is 60 mm2 find the height and base if the triangle

Answers

Answered by abhi569
37

Answer:

10 mm and 12 mm

Step-by-step explanation:

Let the base be 'a' and hence height should be 2 less than 2 or 'a - 2'.

Area of triangle = 1/2 * height * base

Here,

= > 1/2 * a * (a - 2) = 60

= > a( a - 2 ) = 60 * 2

= > a² - 2a = 120

= > a² - 2a - 120 = 0

= > a² - ( 12 - 10 )a - 120 = 0

= > a² - 12a + 10a - 120 = 0

= > a( a - 12 ) + 10( a - 12 ) = 0

= > ( a - 12 )( a + 10 ) = 0

= > a = 12 or - 10

= > a = 12, as a can't be negative.

Hence,

Base = a mm = 12 mm

Height = a - 2 mm = 12-2 = 10 mm

Answered by Anonymous
39

Assume that the base of the triangle is x.

The height of a triangle is 2mm less than the base. So, the height of the triangle is (x - 2) mm.

Area of triangle is 60 mm².

We know that,

Area of triangle = 1/2 × base × height

Substitute values

→ 60 = 1/2 × a × (a - 2)

→ 120 = a² - 2a

→ a² - 2a - 120 = 0

Factorise it,

→ a² - 12a + 10a - 120 = 0

→ a(a - 12) + 10(a - 12) = 0

→ (a - 12)(a + 10) = 0

→ a = 12 and - 10

Side can't be negative.

Hence, the base of the triangle is 12 mm and height is 10 mm (12-2 = 10).

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