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The perimeter of a right-angled triangle is 72 cm. The lengths of its sides are in the ratio 3 : 4 : 5 Work out the area of the triangle.

Let x be a number so that the sides of the triangle are 3x, 4x and 5x, because the ratio is 3 : 4 : 5. The perimeter is 3x+4x+5x=12x=72, meaning that x = 72/12 = 6. The sides of the triangle are 3 6=18, 4 6=...
VP
Answered by Vlad P. • Maths tutor
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Find the roots of x^2-9=0

Stage 1: Identify that the equation is a quadratic and that the question is asking you to find out which values 'x' fit this equation. Quadratics can be written algebraically in the form ax 2 +bx+c and have ...
JD
Answered by Jamie D. • Maths tutor
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Find the length of the hypotenuse of a right angled triangle which has other two sides of length 5 and 12.

When we have 2 sides of a right angled triangle, we can use Pythagoras' Theorem to find the third missing side. This theorem states that if we label the hypotenuse (the side opposite the right angle) as c , ...
AY
Answered by Andrew Y. • Maths tutor
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Find an expression for the nth term of the following sequence: 7, 11, 15, 19

In terms of understanding the question, we are asked to look for a common rule that would help us find any term, or member, of the sequence in the question, no matter how big. The "nth" bit they ta...
LH
Answered by Luke H. • Maths tutor
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solve the inequality x^2-4x+4>0

x 2 -4x+4>0 => (x-2)(x-2)>0. We can illustrate this line on a graph showing a quadratic whose vertex is at (2,0). Therefore, the answer to our inequality is x<2,x>2 (but x does not equal 2) fo...
JA
Answered by James A. • Maths tutor
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