The sides of a right-angled triangle containing the right angle are 4x and (2x - 1) cm. If the area of the triangle is 30cm². Calculate the length of its sides.
Answers
SOLUTION:
Here we have been provided with sides of a right-angled triangle.
- First side = 4x
- Second side = 2x - 1
And area is of 30cm².
We have to calculate the lengths of its sides.
So we would be using formula of calculating the area of triangle,
- A = 1/2 × b × h
Here, h is height and b is base.
We have,
- base = 2x-1 and height = 4x
So using this formula,
⇒30 = 1/2 × (2x - 1) × 4x
⇒ 30 = 1 × (2x - 1) × 2x
⇒ 30 = 2x (2x - 1)
Opening bracket,
⇒ 30 = 2x × (2x - 1)
⇒ 30 = 4x² - 2x
Dividing by 2,
⇒ 15 = 2x² - x
Transposing 15 to R.H.S.,
⇒ 2x² - x - 15 = 0
Forming factors,
⇒ 2x² - 6x + 5x - 15 = 0
Grouping them,
⇒ 2x (x - 3) + 5 (x - 3) = 0
⇒ (x - 3) (2x + 5) = 0
Now,
⇒ x - 3 = 0
⇒ x = 3
And,
⇒ 2x + 5 = 0
⇒ 2x = -5
⇒ x = -5/2
We know that length is never negative.
First side : 4x ⇒ 4 × 3 ⇒ 12cm
Second side : 2x - 1 ⇒ 2 × 3 - 1 ⇒6 - 1 ⇒ 5cm
We would be using Pythagoras theorem now, to find the third side,
Third side : √12² + 5² ⇒√144 + 25⇒√169⇒13cm