The hypotenuse of a right triangle is 10 cm. What is the perimeter of the triangle?
1). The area of the triangle is 25 square cm
2). The triangle is an isosceles triangle
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My answer is D.
i) The area of triangle is 25
xy = 50
y = 50/x
With this relation, using pythagoras, we can find the value of x and y, which will help to find perimeter (10+x+y)
ii) Isosceles triangle
x = y
With this relation also, we can find the value of x as x^2+x^2 = 100.
Afterwards, we can get the value of x and perimeter.
Hence, both statements individually can answer the question.
x^2 + y ^2 = 100
2xy = 100
thus (x – y)^2 = 0
and (x +y) ^2 = 200
x = y
triangle is isoceles
4x^2 = 200
x = sqrt(50) = y
thus the 1st statement can give us the perimeter
the 2nd statement explicitly states that the triangle is isoceles…thus it shall lead to x = y, thus 2x^2 = 100
which also leads to the same result…
both statements independently are sufficient
D
d