Question

Can someone break this down for someone who doesn't understand word problems?


Thanks!


A city lot has the shape of a right triangle whose hypotenuse is 1 ft longer than one of the other sides. The perimeter of the lot is 306 ft. How long is each side of the lot? (Enter your answers as a comma-separated list.)

Answer 1

Let x and y equal the lengths of the sides of the triangle. The phrase "a right triangle whose hypotenuse is 1 ft longer than one of the other sides" tells use several things. A "right triangle" tells us that we are dealing with a triangle with one angle equal to 90 degrees. We also know that the hypotenuse is "1 ft longer than one of the other sides" which implies that the hypotenuse is 1+ one of the sides.....I just chose side x. From the Pythagorean Theorem we know that the square of the hypotenuse is equal to the sum of the squares of the sides. So this means:\[(1+x)^2=x^2+y^2\] Now from "perimeter of the lot is 306 ft" we know that the perimeter of the triangle is equal to the sum of the lengths of all three sides so:\[x+y+(x+1)=306\]So we now have two equations and two unknowns, so use substitution to solve for x and y.