# How do you work out the diagonal measurements of a rectangle?

You should first draw a rectangle and include the measurements. You will notice that each corner of a rectangle make a 90 degree angle with the two arms. When you include the diagonal, you bisect the rectangle into two right-angled triangles — these have 90 degree angles –. Right angled triangles follow phythagoras throem: a^2 + b^2 = c^2 where a, b and c are the sides of the right-angled triangle where c is the hypotenuse — diagonal of the rectangle –. You can use this concept to determine the diagonal measurements of the rectangle Subsituting into the throem where: a = 2.5 m b = 3.5 m c = d m a^2 + b^2 = c^2 (2.5 m)^2 + (3.5 m)^2 = (d)^2 6.25 m^2 + 12.25 m^2 = (d)^2 18.5 m^2 = (d)^2 sqrt [ 18.5 m ] = d 4.3 m = d The measurement of the diagonal is 4.3 metres. To see if this value is accurate we can subsitute the value of 4.3 metres into the phythogras throem. (2.5 m)^2 + (3.5 m)^2 = (4.3 m)^2 6.25 m^2 + 12.25 m^2 = 18.49 m^2 18.5 m^2 = 18.49 m^2 18.5 m^2 = 18.5 m^2 The answer is c