Question

The hypotenuse of a right triangle is 20m. If the difference between the length of the other sides is 4m. Find the sides.

Answer 1

x= 12cm, x=-16cm but side can never be a negative number.so x=12cm is your perpendicular distance(P) according to assumption.
Base distance(B)=x-4 =12-4=8cm

Answer 2

Given:

A right-angled triangle has a hypotenuse of length 20m. The difference between the other two sides of the triangle is 4m.

To Find:

The lengths of the two sides are?

Solution:

The given problem can be solved using the concepts of triangles.

1. The length of the hypotenuse is 20m.

2. Let the base of the triangle be x meters, as the difference between the two sides is 4 meters, the other side will be x + 4 meters.

3. For a right-angled triangle the hypotenuse is given by the formula,

=> Hypotenuse = $\sqrt{(base)^2+(height)^2}$,

4. Substitute the given values in the above formula,

=> 20 = $\sqrt{x^2 + (x+4)^2}$,

=> 20² = x² + (x-4)² ,

=> 400 = x² +x² +8x + 16,

=> 2x² +8x - 384 = 0,

=> x² + 4x - 192 = 0,

=> x² + 16x - 12x - 192 = 0,

=> x(x+16) -12(x-16) = 0,

=> (x+16)(x-12) = 0,

=> x = 12 (OR) x = -16.

=> As the length cannot be negative the value x = -16 is not considered.

5. The lengths of the sides of the triangle are 12, 16 meters respectively.

Therefore, the values of the sides of the triangle are 12, 16 meters respectively.