Part 21 -Worded questions using surds I | Maths Made Easy

# Surds GCSE Maths Revision

## Part 21 -Worded questions using surds I

Example:

A garden has width of 2 cm and length of 3+√5 cm. Calculate the perimeter of the rectangle.

Worked Solution:

Formula for the Perimeter of a rectangle is Perimeter (P)=2×width (w)+2×length (l) i.e. P=2w+2l, if w=2 cm and l=3+√5 cm then:

P=2w+2l=2×2+2(3+√5)=4+2(3+√5)

Expand the bracket and simplify by collecting like terms (for more information on like terms please refer to the “Basic Algebra, formulae and substitution” tutorial):

4+2(3+√5)=4+6+2√5=10+2√5

Hence, P=10+2√5 cm

(note: don’t forget to write the units).

A model garden has width of √5-4 cm and length of 3 cm. Calculate the perimeter of the rectangle.

Your answer can be written in the form $a\sqrt{5}+b$

Find the value of a and b.