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
If the difference between the sides of a right-angled triangle is 3 cm and its area is 54 cm2; find its perimeter.
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 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.
Find the area of a triangle whose sides are 27 cm, 45 cm and 36 cm.
Find the area of a right angled triangle whose hypotenuse is 15cm and the base is 9cm.
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.
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 | ? |
A piece of wire is 36 cm long. What will be the length of each side if we form an equilateral triangle
