Question

the hypotenuse of a right triangle is 3 cm longer than the length of the shorter leg.The longer leg measures 12cm .Find the lengths of the shorter leg and the hypotenuse

Answer 1

draw a picture



use pythagoras's theorem to find x

(x + 3)^2 = x^2 + 12^2


solve for x the shorter side , add 3 to it to get the hypotenuse

Answer 2

\[\large a^2 + b^2 = c^2\]The above is Pythagorean Theorem. We may substitute \(c = a + 3\).\[\large a^2 + b^2 = (a + 3)^2\]Now, we have \(b = 12\).\[\large a^2 + 12^2 = (a + 3)^2 \]\[\implies\large a^2 + 144 = a^2+ 6a + 9 \]

Answer 3

You may subtract \(a^2\) from both sides, which in fact makes it easier!\[\large \implies 6a + 9 = 144\]

Answer 4

is 6a =a 144=b and 9=c?

Answer 5

not quite if 6a + 9 = 144
subtract 9 from both sides

6a = 135

solve for a

Answer 6

a=22.5 which is the hypotenuse ?

Answer 7

or the short leg?

Answer 8

no that is a shorter side..... the hypotenuse is a + 3

Answer 9

so now i plug in my answers to get c squared right?

Answer 10

no you have the length o

a = 22.5

b = 12 ( given)

c = 22.5 + 3 = 25.5 (hypotenuse)

thats all you need

Answer 11

you can check your solution by applying the theorem to

12^2 + 22.5^2 and the answer should be 25.5^2

Answer 12

thank you sorry for the frustration :/

Answer 13

thats ok... I hope it all makes sense

Answer 14

it does now thank you

Answer 15

\[\left( x \right)^2 +\left( 12 \right)^2 = \left( x+3 \right)^2\]

Answer 16

\[x^2 + 144 = x^2 +6x + 9\]

Answer 17

\[x = 135\div6\]

Answer 18

hey mites... the problem as been solved... but thanks for the great work