Advertisements
Advertisements
Question
The perimeter of a triangle is 28 cm. One of it’s sides is 8 cm. Write all the sides of the possible isosceles triangles with these measurements.
Advertisements
Solution
Let ∆ABC be an isosceles triangle, where AB = 8 cm
Case I: If AB = BC
∴ AB = BC = 8 cm
Perimeter of the triangle ABC = 28 cm
⇒ AB + BC + CA = 28 cm
⇒ 8 cm + 8 cm + CA = 28 cm
⇒ 16 cm + CA = 28 cm
⇒ CA = 28 cm – 16 cm = 12 cm
∴ Sides are 8 cm, 8 cm and 12 cm
Case II: If BC = CA
Perimeter of the triangle ABC = 28 cm
⇒ AB + BC + CA = 28 cm
8 cm + 2BC = 28 cm
⇒ 2BC = 28 cm – 8 cm = 20 cm
⇒ BC = 10 cm
∴ Sides are 10 cm, 10 cm and 8 cm
APPEARS IN
RELATED QUESTIONS
Calculate the area and the height of an equilateral triangle whose perimeter is 60 cm.
Find the area of a triangle, whose sides are :
18 mm, 24 mm and 30 mm
Find the area of a triangle, whose sides are :
21 m, 28 m, and 35 m
The base and the height of a triangle are in the ratio 5 : 3. If the area of the triangle is 67.5 m2; find its base and height.
Find the area of a triangle whose sides are 27 cm, 45 cm and 36 cm.
Find the area of a triangle whose sides are in the ratio 5:12:13 and whose perimeter is 36cm.
The perimeter of a triangle is 72cm and its sides are in the ratio 3:4:5. Find its area and the length of the altitude corresponding to the longest side.
The table given below contains some measures of the triangle. Find the unknown values.
| Side 1 | Side 2 | Side 3 | Perimeter |
| 11 feet | ? | 9 feet | 28 feet |
Find the perimeter of An isosceles triangle with equal sides 10 cm each and third side is 7 cm
Find the perimeter of the triangle, whose sides are 13 cm, 5 cm and 14 cm
