I have bad tendency to come up with difficult questions, but a challenge is always good! But just remember your normal procedure with surds and you'll get it right. Spoilers are there for hints.
A right-angled triangle has side length's (2+5) and (9−25)
(i) Find the length of the hypotenuse of this triangle and express it in the form a−b5 where a and b are integers. BONUS: Express the length of the hypotenuse in the form c55−c45 where c is an integer.
Spoiler
(ii) Express 4.1% of the triangle's area in the form BA(c3+55) where A, B and c are integers.
Spoiler
(iii) What is 1.4% of the area you found in part (ii)? Express this in the form (D⋅10−2c)(c3+55) where D is a decimal, and c is an integers.
I have bad tendency to come up with difficult questions, but a challenge is always good! But just remember your normal procedure with surds and you'll get it right. Spoilers are there for hints.
A right-angled triangle has side length's (2+5) and (9−25)
(i) Find the length of the hypotenuse of this triangle and express it in the form a−b5 where a and b are integers. BONUS: Express the length of the hypotenuse in the form c55−c45 where c is an integer.
Spoiler
(ii) Express 4.1% of the triangle's area in the form BA(c3+55) where A, B and c are integers.
Spoiler
(iii) What is 1.4% of the area you found in part (ii)? Express this in the form (D⋅10−2c)(c3+55) where D is a decimal, and c is an integers.
Don't be daunted by the looks of it, have a go and spend however much time you need to complete it. Ask whatever you need at each stage, you already know the methods to find what the questions asks for. This tests you on surds, algebra, fractions, and decimals altogether.
Correct number but wrong sign Notice that you are multiplying negative by a negative there so the answer must be a positive. Other than that, you have now expanded both brackets. Refer back to the Pythagorean theorem and see what you need to do with the two answers you just got.
Correct number but wrong sign Notice that you are multiplying negative by a negative there so the answer must be a positive. Other than that, you have now expanded both brackets. Refer back to the Pythagorean theorem and see what you need to do with the two answers you just got.