Solve the problem.
-The hypotenuse of a right triangle is $\sqrt { 89 } \text { in }$ . The sum of the lengths of the legs is 13 in. Find the lengths of the legs.
A) The legs are 6 in. and 9 in.
B) The legs are 6 in. and 7 in.
C) The legs are 5 in. and 8 in.
D) The legs are 4 in. and 9 in.

Question

Quizplus · Accepted Answer

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). Given that the hypotenuse is $\sqrt{89}$ inches and the sum of the legs is 13 inches, we can set up the equations: $a^2 + b^2 = 89$ and $a + b = 13$. Solving these equations simultaneously, we find that the only pair of positive integers that satisfies both conditions is 5 and 8, making the lengths of the legs 5 inches and 8 inches respectively.

Solve the Problem 89 in \sqrt { 89 } \text { in }89​ in

Solve the Problem $\sqrt { 89 } \text { in }$