Lesson Solved problems on the perimeter and side lengths of a triangle
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<H2>Solved problems on the perimeter and side lengths of a triangle</H2> This lesson is a small collection of typical comparatively simple problems on finding dimensions of a triangle sides. The goal of this text is to teach you by examples to make first steps in this area. <H3>Problem 1</H3>The second side of a triangle is 5 feet longer than the shortest side and the third side is 5 feet shorter than twice the length of the shortest side. If the perimeter is 52 ft, what are the lengths of the three sides? <B>Solution</B> Let <B>x</B> be length of the shortest side of the triangle, in feet. Then the second side has the length of (x+5) feet, and the third side has the length of (2x-5) feet. So the perimeter of the triangle is x + (x+5) + (2x-5) = 4x. Thus you have an equation 4x = 52, according to the condition. Hence, x = {{{52/4}}} = 13. It is the length of the shortest side in feet. The second side is 13 + 5 = 18 ft long, and the third side is 2*13 - 5 = 21 ft. <B>Answer</B>. The first side is 13 ft long, the second side is 18 ft and the third side is 21 ft. <H3>Problem 2</H3>The longest side of a triangle is 5 inches longer than the shortest side. The medium side is 4 inches longer than the shortest side. If the perimeter of the triangle is 27 inches, what are the lengths of the three sides? <B>Solution</B> Let <B>x</B> be length of the shortest side of the triangle, in inches. Then the longest side has the length of (x+5) inches. The medium side has the length of (x+4) inches. So the perimeter of the triangle is x + (x+5) + (x+4) = 3x+9. Thus you have an equation 3x + 9 = 27, according to the condition. Hence, 3x = 27 - 9 = 18, x = {{{18/3}}} = 6. It is the length of the shortest side in inches. The longest side is 6 + 5 = 11 in long, and the medium side is 6 + 4 = 10 in. <B>Answer</B>. The shortest side is 6 in long, the longest side is 11 in and the medium side is 10 in. <H3>Problem 3</H3>Two sides of a triangle have the same length. The third side measures 3 m less than twice that length. The perimeter of the triangle is 13 m. Find the lengths of the three sides. <B>Solution</B> As you understand, the triangle is isosceles. Let <B>x</B> be length of any of its two congruent lateral sides. Then the third side has the length of (2x-3) feet. So the perimeter of the triangle is x + x + (2x-3) = 4x - 3. Thus you have an equation 4x - 3 = 13, according to the condition. Hence, 4x = 13 + 3 = 16, and x = {{{16/4}}} = 4. It is the length of any of the two lateral sides in feet. The third side is 2*4 - 3 = 5 ft long. <B>Answer</B>. The two lateral sides are 4 ft long each, the third side is 5 ft. <H3>Problem 4</H3>A triangle has a perimeter of 84 centimeters. Each of the two longer sides of the triangle is three times as long as the shortest side. Find the length of each side of the triangle. <B>Solution</B> Again, the triangle is isosceles. Let <B>x</B> be length of any of its shortest side (which is the base, of course), in centimeters. Then any of the two lateral sides has the measure of 3x centimeters. So the perimeter of the triangle is x + 3x + 3x = 7x. Thus you have an equation 7x = 84, according to the condition. Hence, x = {{{84/7}}} = 12. It is the length of the base side of the triangle in centimeters. Hence, each of the two lateral sides is 3*12 = 36 cm long. <B>Answer</B>. The two lateral sides are 36 cm long each, the base side is 12 cm. My other closely related lessons in this site are - <A HREF=http://www.algebra.com/algebra/homework/Points-lines-and-rays/Solved-problems-on-the-perimeter-and-side-lengths-of-a-right-angled-triangle.lesson>Solved problems on the perimeter and side lengths of a right-angled triangle</A> - <A HREF=http://www.algebra.com/algebra/homework/Points-lines-and-rays/Solved-problems-on-the-perimeter-and-side-lengths-of-a-parallelogram.lesson>Solved problems on the perimeter and the side lengths of a parallelogram</A> - <A HREF=http://www.algebra.com/algebra/homework/Points-lines-and-rays/Solved-problems-on-the-perimeter-and-side-lengths-of-a-rectangle.lesson>Solved problems on the perimeter and side lengths of a rectangle</A> - <A HREF=http://www.algebra.com/algebra/homework/Points-lines-and-rays/OVERVIEW-of-lessons-on-perimeter-and-side-lengths-of-triangles-parallelograms-and-rectangles.lesson>OVERVIEW of lessons on perimeter and side lengths of triangles, parallelograms and rectangles</A> Use this file/link <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A> to navigate over all topics and lessons of the online textbook ALGEBRA-I.
