Advertisements
Advertisements
Question
The perimeter of an isosceles triangle is 42 cm and its baše is (32) times each of the equal sides. Find the length of each side of the triangle, area of the triangle and the height of the triangle.
Advertisements
Solution
Let ‘x’ be the measure of each equal sides
∴ Base =`3/2x`
`∴x + x + 3/2x= 42 ` [∵ Perimeter = a + b + c = 42 cm]
`⇒7/2x=42 `
`⇒x= 12cm`
∴Sides are a = x = 12 cm
b = x = 12 cm
`c=x=3/2(12)cm = 18 cm`
By heron’s formulae
∴ Area of triangle =`sqrt(s(s-a)(s-b)(s-c)) cm^2`
=`sqrt(21(9)(9)(21-18)cm^2)`
=`sqrt((21)(9)(9)(3))cm^2`
=`71.42cm^2`
`∴ Area of triangle = 71.42 cm^2`
APPEARS IN
RELATED QUESTIONS
A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?
Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.
A rhombus sheet, whose perimeter is 32 m and whose one diagonal is 10 m long, is painted on both sides at the rate of Rs 5 per m2. Find the cost of painting.
If the points A(– 3, 9), B(a, b) and C(4, – 5) are collinear and if a + b = 1, then find a and b
A triangular shaped glass with vertices at A(– 5, – 4), B(1, 6) and C(7, – 4) has to be painted. If one bucket of paint covers 6 square feet, how many buckets of paint will be required to paint the whole glass, if only one coat of paint is applied
Find the area of triangle AGF
Find the area of triangle FED
If (5, 7), (3, p) and (6, 6) are collinear, then the value of p is
From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 14 cm, 10 cm and 6 cm. Find the area of the triangle.
The sides of a quadrilateral ABCD are 6 cm, 8 cm, 12 cm and 14 cm (taken in order) respectively, and the angle between the first two sides is a right angle. Find its area.
