Question

A right -angled triangle has an area of 56cm^(2). The width of the triangle is n+4cm. The height is 6cm less than the width. Find the value of n.

Answer 1

n = 10

Explanation:

the area (A) of a triangle is calculated as

A =
`(1)/(2)` bh ( b is the base and h the height )

here b = n + 4 , height = n + 4 - 6 = n - 2 and A = 56 , then

`(1)/(2)` (n + 4)(n - 2) = 56 ← multiply both sides by 2 to clear the fraction

(n + 4)(n - 2) = 112 ← expand factors using FOIL

n² + 2n - 8 = 112 ( subtract 112 from both sides )

n² + 2n - 120 = 0 ← in standard form

(n + 12)(n - 10) = 0 ← in factored form

equate each factor to zero and solve for n

n + 12 = 0 ⇒ n = - 12

n - 10 = 0 ⇒ n = 10

however, n > 0 , then n = 10