Question

The three sides of a right-angled triangle are proportional to the numbers 3, 4 and 5. Find the length of each side knowing that the area of the triangle is 24 m².

• A.
• B.
• C. 6m, 8m, 12m
• D. 2m, 4m, 6m

Answer 1

The correct option is A

Let the length = x m

Since the shorter side = 3x m [Base]

Longer side = 4x m [Height]

Third side = 5x m

Area of triangle = $\frac{1}{2}\times Base\times Height$

$24=\frac{1}{2}\times 3x\times 4x$

$x^2=4$

$\to$ x = 2 or x = -2

Since, side can't be negative.

Therefore, x =2

Now,

Length of base = 3x = 6m

Length of height = 4x = 8m

Length of hypotenuse = 5x = 10m