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31 votes
31 votes
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 =

User TonyParker
by
2.8k points

1 Answer

9 votes
9 votes

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

User H W
by
2.9k points