In triangle ABC, angle B is a right angle. The length of side AB is 10√37 and the length of side BC is 24√37. What is the length of the side AC?
Correct answer: B. 26√37
- A. 14√37
- B. 26√37
- C. 34√37
- D. √(34.37)
Explanation
Choice B is correct. The Pythagorean theorem states that for a right triangle, c2 = a2 + b2, where c represents the length of the hypotenuse and a and b represent the lengths of the legs. It's given that in triangle ABC, angle B is a right angle. Therefore, triangle ABC is a right triangle, where the hypotenuse is side AC and the legs are sides AB and BC. It's given that the lengths of sides AB and BC are 10√37 and 24√37, respectively. Substituting these values for a and b in the formula c2 = a2 + b2 yields c2 = (10√37)2 + (24√37)2, which is equivalent to c2 = 100(37) + 576(37), or c2 = 676(37). Taking the square root of both sides of this equation yields c = +,- 26√37. Since c represents the length of the hypotenuse, side AC, c must be positive. Therefore, the length of side AC is 26√37.
Report an error
The more specific you are, the faster it gets fixed. A source beats an opinion.
Prefer email? support@testustad.com
About Quantitative Reasoning
Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.
Practise Quantitative Reasoning
625 free Quantitative Reasoning MCQs from Analytical and Logical Reasoning, each with the correct answer and an explanation. Unlimited attempts, no account needed.
Discussion
Stuck on an option, or know a faster way to get there? Ask or explain it here.
No comments yet. Be the first to explain this one.
Exams that ask Analytical and Logical Reasoning questions like this
Analytical and Logical Reasoning is on 27 papers prepared for on TestUstad, and all of them draw the same bank, so this question is worth knowing for every one of them.
More Quantitative Reasoning questions
(x - 2) - 4 (y + 7) = 117(x - 2) + 4 (y + 7) = 442The solution to the given system of equations is (x, y). What is the value of 6(x - 2)?
If 48c = 3√47, what is the value of c?
The table shows the linear relationship between the number of cars, c, on a commuter train and the maximum number of passengers and crew, p, that the train can carry. Which equation represents the linear relationship between c and p?
x = y - 3x/2 + 2y = 6Which ordered pair (x, y) satisfies the system of equations shown above?
If f(x) = x2 - 6x + 3 / x - 1, what is f (-1)?
Marisa needs to hire at least 10 staff members for an upcoming project. The staff members will be made up of junior directors, who will be paid $640 per week, and senior directors, who will be paid $880 per week. Her budget for paying the staff members is no more than $9,700 per week. She must hire at least 3 junior directors and at least 1 senior director. Which of the following systems of inequalities represents the conditions described if x is the number of junior directors and y is the number of senior directors?