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