Advertisements
Advertisements
Question
Each equal side of an isosceles triangle is 3cm less than the unequal side. The height of the perpendicular from the vertex to the unequal side is 3cm less than the equal side. If the area of the isosceles triangle is 108cm2, find the perimeter of the triangle.
Solution
Let the unequal side of the Isosceles triangle = x
Then the equal side of the Isosceles triangle = x - 3
And the perpendicular to the unequal side from the opposite vertex = x - 6
We know that, Area of a Triangle
= `(1)/(2)"b.h" "i.e"(1)/(2)("Base" xx "Height")`
∴ Area of the Isosceles Triangle
= `(1)/(2) xx(x - 6)`
= 108
⇒ x2 - 6x = 216
⇒ x2 - 6x - 216 = 0
⇒ x2 - 6x + 9 - 9 - 216 = 0
⇒ (x - 3)2 = 225
⇒ x - 3 = 15
⇒ x = 18
⇒ x - 3 = 15
⇒ Perimeter
= 18 + 15 + 15
= 48cm.
APPEARS IN
RELATED QUESTIONS
Find the area of an equilateral triangle of side 20 cm.
Find the area of an equilateral triangle having perimeter of 18cm.
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 a rectangle whose sides are in the ratio of 1 : 3
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
A chessboard contains 64 equal square and the area of each square is 6.25cm2. A 2cm wide border is left inside of the board. Find the length of the side of the chessboard.
The cross-section of a canal is a trapezium in shape. If the canal is 10m wide at the top, 6m wide at the bottom and the area of cross-section is 72 sq.m, determine its depth.
If in an isosceles triangle, each of the base angles is 40°, then the triangle is ______.
In an isosceles triangle, angles opposite to equal sides are ______.
Two line segments are congruent, if they are of ______ lengths.
