Geometry word problem?

Question

The lengths of the sides of a right triangle are such that the shortest side is 7 in. shorter than the middle side, while the longest side(the hypotenuse) is 1 in. longer than the middle side. Find the lengths of the sides. Please help me with this problem. Thanks.

Answer 1

Let middle side be x units long. Then :

Shortest side = x - 7
Longest side = x + 1

By Pythagoras' Theorem: x^2 + (x-7)^2 = (x+1)^2

Simplifying this quadratic equation: X^2 - 16X + 48 = 0

(X-12) (x-4) = 0 - Hence x = either 4 or 12

Now in case X is 4 then the shortest side comes out as -ve
(X-7 = 4 - 7 = -3)

Thus X = 12

The sides are: 12 - 7; 12; 12 + 1

or 5, 12, 13 units

Thanks

Answer 2

use the formula a2 + b2 = c2 so a is the shortest side which is 7 in your case and the hypotenuse is c which is in your case 1 and u r trying to find out for b ? right ok .. so all you do is plug in the numbers like this 7square +b2=1squared
49 + b2 = 1
-49 -49 subtract 49 from both sides 0 b2 = -48 then u take the square root of each side which means (take off the square) like this
so b2 when u square that it's left b = now u take the square root of 48 (let's c _/```` < this thingy u know what i mean lol and the answer is 3.87 so round it off and it's 4

Answer 3

Start by defining the unknowns...

a = middle side (a)
a - 7 = shortest side (b)
a + 1 = hypotenuse (c)

Since you know it's a right triangle, you can use the pythagorean theorum... a squared plus b squared = c squared.

(a)^2 + (a-7)^2 = (a+1)^2

Now use your algebra... good luck!

Answer 4

let x be the length of the shortest side
the middle side is x+7
the longest side is x+8
(x+7)sq.+(x)sq.=(x+8)sq.
You solve the equation you will get x then +7 you get the middle side and +8 u get the longest side.
good luck!

Answer 5

When you solve that algebraic expression, you may get more than one answer. Pick the one that makes sense.