The perimeter of an isosceles triangle is 50 cm . The base is 11 cm longer then one of the equal sides. Find the sides of the triangle.
Answers
Answer:
The sides of the triangle are 13 cm, 13 cm and 24 cm.
Step-by-step-explanation:
NOTE: Refer to the attachment for the diagram.
We have given that,
Perimeter of isosceles triangle = 50 cm
In figure, △ABC is an isosceles triangle.
BC is base of triangle.
AB = AC
BC = 11 + AB - - - ( 1 ) [ Given ]
Let AB = AC = x cm
Now, we know that,
Perimeter of isosceles triangle = 2 × side + base
⇒ P ( △ABC ) = 2 × AB + BC
⇒ 50 = 2 * x + ( x + 11 ) - - [ From ( 1 ) ]
⇒ 50 = 2x + x + 11
⇒ 50 = 3x + 11
⇒ 3x = 50 - 11
⇒ 3x = 39
⇒ x = 39 ÷ 3
⇒ x = 13
Now,
AB = AC = x
∴ AB = AC = 13 cm
Now,
BC = 11 + AB - - [ From ( 1 ) ]
⇒ BC = 11 + 13
⇒ BC = 24
∴ The sides of the triangle are 13 cm, 13 cm and 24 cm.
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Additional Information:
1. Triangle:
A geometric figure formed by binding three segments and having three corners is called a traingle.
2. Types of triangle:
A. Based on angles
B. Based on sides
3. Based on angles:
A. Acute angled triangle ( < 90° )
B. Right angled triangle ( 90° )
C. Obtuse angled triangle ( > 90° )
4. Based on sides:
A. Equilateral triangle
All sides are equal.
B. Isosceles triangle
Two sides are equal.
C. Scalene triangle
None of the three sides is of equal measures.
