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
Calculate the area and the height of an equilateral triangle whose perimeter is 60 cm.
The given figure shows a right-angled triangle ABC and an equilateral triangle BCD. Find the area of the shaded portion.
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 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.
Use the information given in the adjoining figure to find :
(i) the length of AC.
(ii) the area of an ∆ABC
(iii) the length of BD, correct to one decimal place.
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 cost of fencing a triangular field at the rate of Rs.15 per m is Rs.900. If the lengths of the triangle are in the ratio 3:4:5, find the area of the triangle and the cost of cultivating it at Rs.48 per kg sq.m.
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 and the area of a right angled triangle whose sides are 6 feet, 8 feet and 10 feet
Find the perimeter of A scalene triangle with sides 7 m, 8 m, 10 m
