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The perimeter of a right-angled triangle is 60cm. The lengths of its sides are in the ratio 3:4:5. Work out the area of the triangle.

Draw out a diagram of a right angled triangle. As the lengths of the sides of the triangle are in the ratio 3:4:5, start off by saying each side is 3cm (a), 4cm (b) and 5cm (c) respectively, with 5cm being t...
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Answered by Eadaoin D. • Maths tutor
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Split 1/x^2-1 into partial fractions

First we need to factorise the denominator into (x-1)(x+1). Now we identify that 1/(x-1)(x+1) is equivalent to A/(x-1) + B/(x+1) and now we solve to find the values of A and B. By simplifying the equivalent ...
TM
Answered by Thomas M. • Maths tutor
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Solve x^2-5x+6=0

We can factorise into (x-3)(x-2)=0 to get x=3 and x=2 as solutions for this equation.
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Answered by Thomas M. • Maths tutor
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Simplify the following fraction - Numerator = 2(8-k) + 4(k-1) Denominator = k^2 - 36

The first task is to multiply out the brackets in the numerator. By doing this, we find that the numerator is equivalent to "12 + 2k". We should now simplify the denominator. We can convert it into...
ML
Answered by Matteo L. • Maths tutor
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Solve for x: logx(25) = log5(x)

logx(25) = log5(x)2logx(5) = log5(x)2/log5(x) = log5(x)2 = (log5(x))^2sqrt(2) = log5(x)x = 5^sqrt(2)
Answered by • Maths tutor
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