The hypotenuse of a right triangle is 17 cm and the longer leg is 7 cm greater than the shorter leg. Find the area of the triangle

Question

This is from a math quiz in Algebra 1. I didn't understand the problem

Answer 1

Here you have to take advantage of knowing you are solving a right-angle triangle. This means that the Pythagorean Theorem (a² + b²= c²). In this case a=x cm, b=(x+7) cm and c=17 cm. Once you solve for x, you will know the base (a) and the height (b). 

 

You are now ready to find the area using the equation area= 1/2 base x height= 1/2 a x b. Remember that units on area are cm² (this is because you are multiplying cm x cm).

Answer 2

Actually, you don't know the length of the other leg. You do use the Pythagorean theorem, knowing that your hypotenuse is 17 cm.  You know that one leg has unknown length "x" cm, and the longer leg has length "x + 7" cm.

Answer 3

The area of a triangle is:

 

A = (1/2)*base*height

 

In a right triangle, either of the legs can be the base and the other leg is the height.  You know one of the legs equals 7 cm.  You can find the other leg using the Pythagorean Theorem: √(17² - 7²).  Now you have what you need to find the area.