Advertisements
Advertisements
प्रश्न
The base of an isosceles triangle is 24 cm and its area is 192 sq. cm. Find its perimeter.
Advertisements
उत्तर
It is given that
Area = 192 sq.cm
base = 24 cm
Knowing the length of the equal side, a and base, b of an isosceles triangle, the area can be calculated using the formula,
A = `1/4 xx b xx sqrt (4a^2 - b^2`
Let 'a' be the length of an equal side.
Area = `1/4 xx b xx sqrt(4a^2 - b^2)`
192 = `1/4 xx 24 xx sqrt(4a^2 - 576)`
192 = `6 sqrt(4a^2 - 576)`
`sqrt(4a^2 - 576` = 32
4a2 – 576 = (32)2
4a2 – 576 = 1024
4a2 = 1024 + 576
4a2 = 1600
a = 20 cm
Hence, perimeter = 20 + 20 + 24
= 64 cm
संबंधित प्रश्न
Find the area of an equilateral triangle of side 20 cm.
Find the area of the shaded region in the figure as shown, in which DPQS is an equilateral triangle and ∠PQR = 90°.
Find the area of an isosceles triangle whose perimeter is 72cm and the base is 20cm.
Find the base of an isosceles triangle whose area is 192cm2 and the length of one of the equal sides 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
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.
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, angles opposite to equal sides are ______.
