Dimensions of a Right Triangle The shortest s...

Question

Dimensions of a Right Triangle The shortest side of a right triangle 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.

Right triangle with sides labeled x, x minus 7, and x plus 1, showing a right angle at the shortest side.

Accepted Answer

In a direct triangle. ABC. The measure of the shortest side A B is one inch shorter than the measure of the middle side AC. And the measure of a pot news BC is eight inches longer than the measure of the middle side AC find the measures of A B AC M BC. And so the intro gave us a bunch of information we can use to set up this problem. We have A B AC NBC. Now it tells us A B is shorter than AC and BC is longer than AC. As a result, we will say AC is some length X that we don't know AB is one shorter than ac. All set in a B is X -1 BC is 8" longer, Say BC is X-plus eight. Now, we can make use of the Pythagorean formula here side one A B squared plus side two AC square. It equals to BC squared, four x -1 Squared plus X squared as equals to X plus eight squared. Now we can expand these X -1 Squared, expands to text squared minus X minus X plus one. Bring down our X squared on the right side, this expands to X squared plus eight X plus eight X plus 64. Combining all of these get X squared minus two X plus one plus X squared equals to X squared plus 16 X plus 64. Left side, we get two X squared minus two X plus one. This equals to X squared plus 16 X plus 64. Now, to solve this, we want all of our terms on one side, the equal sign, we'll subtract everything from the right and move it over to the left five X squared 16 X and 64. This will give us X squared minus 18, X minus As equals to zero. Now we have this polynomial. Let's try and factor out and determine what our X is equals to. Well, we look at X X, We have 63 as our seat. So we need to find the factors of 63 as well. 63, negative 63 has negative 1, 63 -63, positive one 21 negative three, negative 21 positive three 9, -7, -9, positive seven. Now we need to find out which of these pairs adds up to equal -18. What we notice here -21, positive three will add up to -18. So we will then take a 21 and positive three set. The whole thing equals to zero. We cannot split up our expression here. X -21 is equal to zero, X-plus three is equal to zero. Solving for zero, we will then get X is equals to 21. X is equals to negative three will disregard our negative answer because we can't have a negative length, Meaning we have X is equals to 21. For other words, R ac Will be 21. RAB is X -1 makes A B equals to 20. Finally BC X plus eight, 21 Plus eight is 29. We can't simplify any farther. So the answer our problem A.B. 20 ac equals 21. NBC is equal to 29. This corresponds with answer A OK. I hope to help you solve the problem. Thanks for watching. Goodbye.

Dimensions of a Right Triangle The shortest side of a right triangle 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.

Key Concepts

Pythagorean Theorem

Algebraic Expressions and Variables

Solving Quadratic Equations

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