Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
If the difference between the sides of a right-angled triangle is 3 cm and its area is 54 cm2; find its perimeter.
ABC is a triangle in which AB = AC = 4 cm and ∠A = 90°. Calculate:
(i) The area of ΔABC,
(ii) The length of the perpendicular from A to BC.
Find the area of an isosceles triangle with perimeter is 36 cm and the base is 16 cm.
Two sides of a triangle are 6 cm and 8 cm. If the height of the triangle corresponding to 6 cm side is 4 cm; find :
(i) area of the triangle
(ii) height of the triangle corresponding to 8 cm side.
The sides of a triangle are 16 cm, 12 cm, and 20 cm. Find :
(i) area of the triangle ;
(ii) height of the triangle, corresponding to the largest side ;
(iii) height of the triangle, corresponding to the smallest side.
The lengths of the sides of a triangle are in the ratio 4: 5 : 3 and its perimeter is 96 cm. Find its area.
Find the area of a triangle with a base 12cm and a height equal to the width of a rectangle having area of 96cm2 and a length of 12cm.
Find the perimeter of An isosceles triangle with equal sides 10 cm each and third side is 7 cm
In the following figure, all triangles are equilateral and AB = 8 units. Other triangles have been formed by taking the mid points of the sides. What is the perimeter of the figure?
Find the perimeter of a triangle with sides measuring 10 cm, 14 cm and 15 cm.
