How big is a right-angled triangle's area? I.The triangle's perimeter is 30 cm. II. The triangle's base and height have a 5:12 ratio. III.The size of the triangle is the same as the area of a 10 cm long rectangle.
A. I and II only
B. II and III only
C. I and III only
D. III, and either I or II only
Answer:A
How big is a right-angled triangle's area? I.The triangle's perimeter is 30 cm. II. The triangle's base and height have a 5:12 ratio. III.The size of the triangle is the same as the area of a 10 cm long rectangle.
A. I and II only B. II and III only C. I and III only D. III, and either I or II only
Explanation: From II, height = 5:12 as a basic .Let's say the base is 5x and the height is 12x.The hypotenuse is thus equal to (5x)2 + (12x)2 = 13x.The triangle's circumference is 30 cm, according to I.30 x = 5x + 12x + 13x = 5x + 12x + 13x = 5x + 12x + 13x = 5x + 12.As a result, the base is 5x = 5 cm, and the height is 12x = 12 cm.30 cm2 area = 1/2 x 5 x 12 cm2.As a result, the solution is given by combining I and II.Because the rectangle's width is not specified, III is clearly redundant.