the height of a triangle is 7 cm less than its base.And its area is 9 sq. cm Find the height and base of the triangle
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Given in the question that the base (b) of the triangle is 7 cm less than the height (h) of the triangle and the area of the triangle is 9 cm².
=> b = h - 7
The area of the triangle = (1/2) × base × height
=> (1/2) × b × h = 9
=> h × (h-7) = 18 {substituting b = h-7}
=> h² - 7h -18 = 0
=> h² - 9h + 2h -18 = 0
=> h(h-9) +2(h-9) = 0
=> h = 9 , -2
Value of h = 9 cm as the value height of a triangle cannot be negative.
b = 9 -7 = 2 cm
Height of the triangle = 9 cm
Base of the triangle = 2 cm
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