A right-angled triangle has an area of
45 cm².
The width of the triangle is n + 3 cm.
The height is 9 cm less than the width.
45 cm²
n + 3
Find the value of n.
n =

Question

A right-angled triangle has an area of  45 cm².  The width of the triangle is n + 3 cm.  The height is 9 cm less than the width.  45 cm²  n + 3  Find the value of n.  n =

Orla · Answer

Answer:    A = 1/2 width × height   width = n + 3 cm  height = width - 9 cm  height = n + 3cm - 9cm  height = n - 6cm    A = 1/2 width × height     = 1/2 (n + 3cm) × (n  - 6cm)  45cm^2 ×2 = n^2 - 3ncm - 18cm^2  n^2 - 3ncm - 18cm^2 - 90cm^2 = 0  n^2 - 3ncm - 108cm^2 = 0  Find two numbers that their sum is -3 and their product is 108. Therefore, the numbers could be -12 and 9   n^2 - 3ncm - 108cm^2 = 0  n^2 - 12ncm + 9ncm - 108cm^2 = 0  n(n - 12cm) + 9cm(n - 12cm) = 0  (n - 12cm) (n + 9cm) = 0  Either (n - 12cm) = 0 or (n + 9cm) = 0  n = 12cm or n = -9cm  but  n = -9cm is invalid because there is no negative distance.   n = 12cm is the answer

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