find the sides of triangle

Question

angle A =90 degree, AB =xcm, AC =x+5, area =150cm 

Answer 1

Since A is 90°, the triangle is a right triangle.  That means that the area is 1/2 the product of the legs.

 

The legs are x and x + 5, so the area, 1/2 the product of the legs, is x(x+5)/2.  That's equal to 150.  That gives us an equation:

x(x+5)/2 = 150

x(x+5) = 300

x² + 5x = 300

x² + 5x - 300 = 0

(x - 15)(x + 20) = 0

 

So x = 15 or x = -20

 

Since a side can't be negative, the solution that makes sense is x = 15.

 

So AB = 15 and AC = 20.

 

But what about the hypotenuse, BC?  Use the Pythagorean Theorem:

 

AB² + AC² = BC²

15² + 20² = BC²

225 + 400 = BC²

625 = BC²

25 = BC

 

So the sides are 15, 20, and 25