Advertisements
Advertisements
प्रश्न
Find the area of an isosceles triangle ABC in which AB = AC = 6 cm, ∠A = 90°. Also, find the length of perpendicular from A to BC.
Advertisements
उत्तर
Area of ΔABC
= `(1)/(2) xx "AB" xx "AC"`
= `(1)/(2) xx 6 xx 6`
= 18cm2.
In right-angled ΔBAC,
BC2
= AB2 + AC2
= 62 + 62
= 36 + 36
= 72
⇒ BC = `6sqrt(2)"cm"`
Now,
area of ΔABC is also
= `(1)/(2) xx "BC" xx "AP"`
⇒ 18 = `(1)/(2) xx 6sqrt(2) xx "AP"`
⇒ 18 = `3sqrt(2) xx "AP"`
⇒ AP
= `(18)/(3sqrt(2)`
= `(6)/sqrt(2)`
= `(6)/sqrt(2) xx sqrt(2)/sqrt(2)`
= `(6sqrt(2))/(2)`
= `3sqrt(2)"cm"`.
APPEARS IN
संबंधित प्रश्न
Find the area of an equilateral triangle of side 20 cm.
The area of an equilateral triangle is numerically equal to its perimeter. Find the length of its sides, correct two decimal places.
In a right-angled triangle PQR right-angled at Q, QR = x cm, PQ = (x + 7) cm and area = 30 cm2. Find the sides of the triangle.
In a right-angled triangle ABC, if ∠B = 90°, AB - BC = 2 cm; AC - BC = 4 and its perimeter is 24 cm, find the area of the triangle.
Find the area of an isosceles triangle whose perimeter is 72cm and the base is 20cm.
A wire when bent in the form of a square encloses an area of 16 cm2. Find the area enclosed by it when the same wire is bent in the form of an equilateral triangle
Each of the equal sides of an isosceles triangle is 4 cm greater than its height. If the base of the triangle is 24 cm; calculate the perimeter and the area of the triangle.
If in an isosceles triangle, each of the base angles is 40°, then the triangle is ______.
In an isosceles triangle, two angles are always ______.
Two line segments are congruent, if they are of ______ lengths.
