if the legnth of the hypotenuse of a right triangle is 13. the length of the shorter leg is 7 less than the lenth of the smaller leg. How do i find the length of the shorter leg

Question

campbell_st · Answer

well set up an equation let the smaller leg be x

then the shorter leg is x - 7

so using pythaoras' theorem you have 

$$(x -7)^2 + x^2 = 13^2$$

now you need to simplify then solve the equation.

anonymous · Answer

that would be x squared-49 plus x2 equals 13 squared right?

campbell_st · Answer

not quite you have a perfect square so its 

$$x^2 - 14x + 49 + x^2 = 169$$

anonymous · Answer

hmm i have 0 idea how to solve this

campbell_st · Answer

ok... so you get 

$$2x^2 - 14x - 120 = 0$$

divide each term by 2

$$x^2 - 7x - 60 = 0$$

do you know how to factor quadratics equations..?

anonymous · Answer

the smallest leg would be 5 correct?

campbell_st · Answer

correct.... its a pythagorean triad...

anonymous · Answer

could u also tell me this. it says the length of an equilateral triangle is 4. find he length of the altitude.

campbell_st · Answer

ok... so the altitude will be perpendicular to a side here is a reference site that explains altitude http://www.mathopenref.com/altitude.html the triangle looks like |dw:1380663039970:dw|

anonymous · Answer

what would the formula be?

campbell_st · Answer

its pythaoras' theorem again, you have a hypotenuse of 4 and short side of 2, find the other short side

anonymous · Answer

ok and another question is the side of one square is 3 inches longer than the side of a second square.if the sum of their areas is 130 inches squared, find the legnth of the side of each square.