# Question #22db6

##### 3 Answers

I found

#### Explanation:

I would call the longer leg

Using Pythagoras we get:

so:

Using the Quadratic Formula:

so:

we use the positive one, giving the length of the longer length as

shorter leg = 5

#### Explanation:

Since this is a right triangle , we can use

#color(blue)" Pythagoras's theorem " # If h represents the hypotenuse and a , b the other 2 sides then

# h^2 = a ^2 + b^2# here , let the longer arm = x , so shorter one is then (x-7)

substitute values into formula :

hence

#13^2 = x^2 + (x-7)^2 = x^2 + x^2-14x + 49# so

#2x^2 - 14x + 49 = 169 # This is a quadratic function so equate to zero to solve.

#2x^2 - 14x - 120 = 0 # factorising:

#2(x^2 - 7x - 60 ) = 0 # To factor

#x^2-7x-60# require factors of -60 which sum to -7

These are 5 and - 12

#rArr 2(x-12)(x+5) = 0 rArr x = -5 , x = 12# now x > 0 hence x = 12 and so short leg = x-7 = 12 - 7 = 5

The length of shorter length is

#### Explanation:

Consider the diagram

Use the **pythagoras theorem**

#color(brown)(x^2+y^2=h^2#

Where,

**Hypotenuse**

**other two sides**

Use the formula

Factor it out

Remove the

If you solve for it you get,

#x=12,-5#

#x>0:.x=12#

#x=12,x-7=12-7=5#