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
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
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).