Advertisements
Advertisements
प्रश्न
Area of an isosceles triangle is 48 cm2. If the altitudes corresponding to the base of the triangle is 8 cm, find the perimeter of the triangle.
Advertisements
उत्तर
Given, area of ΔABC = 48 cm2 and altitude = 8 cm
∵ ΔABC is an isosceles triangle, where AB = AC
∴ Area of ΔABC = `1/2` × BC × AD = 48 ...[∵ Area of triangle = Base × Height]
⇒ 48 = `1/2` × BC × AD
⇒ `1/2` × BC × 8 = 48
⇒ BC = `(48 xx 2)/8`
BC = 12 cm
Now, in an isosceles triangle, BD = DC = 6 cm ...[∵ AD ⊥ BC]
Applying Pythagoras theorem in right-angled ΔADB,
AB2 = BD2 + AD2
⇒ AB2 = 62 + 82 = 36 + 64
⇒ AB2 = 100
⇒ AB = 10 cm
Now, perimeter of triangle = AB + AC + BC
= AB + AB + BC ...[∵ AB = AC]
= 10 + 10 + 12
= 32 cm
APPEARS IN
संबंधित प्रश्न
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.
The altitude and the base of a triangular field are in the ratio 6: 5. If its cost is ₹ 49,57,200 at the rate of ₹ 36,720 per hectare and 1 hectare = 10,000 sq. m, find (in metre) dimensions of the field.
Find the area of a triangle whose base is 3.8 cm and height is 2.8 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 |
| 6 cm | 5 cm | 2 cm | ? |
Find the perimeter of A scalene triangle with sides 7 m, 8 m, 10 m
The scalene triangle has 40 cm as its perimeter and whose two sides are 13 cm and 15 cm, find the third side
Find the perimeter of the triangle, whose sides are 13 cm, 5 cm and 14 cm
