Advertisements
Advertisements
Question
The area of the isosceles triangle is 60 cm2, and the length of each one of its equal side is 13cm. Find its base.
Advertisements
Solution
Area of a isosceles triangle = `("b" xx sqrt (4"a"^2 - "b"^2))/4`
Here, area = 60, a = 13. Putting this in equation and squaring both sides, we get
(60 x 4)2 = b2 (4 x 13 x 13 - b2 )
⇒ 57600= b2 x (676 - b2) = 676 b2 - b4
⇒ b4 - 676b2 +57600 = 0
⇒ b4 -100b2 - 576b2 + 57600 = 0
⇒ b2 (b2 - 100) - 576 (b2 - 100) = 0
⇒ (b2 - 100 )(b2 - 576) = 0
⇒ b2 = 576 , b2 = 100
⇒ b = 24 , b = 10
⇒ Hence base can be either 24 or 10 cm.
APPEARS IN
RELATED QUESTIONS
Solve for x: `(x-3)/(x-4)+(x-5)/(x-6)=10/3; x!=4,6`
Solve the following quadratic equations by factorization:
`3x^2-2sqrt6x+2=0`
The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 124. Determine their present ages.
Car A travels x km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol.
Write down the number of litres of petrol used by car A and car B in covering a distance of 400 km.
Solve the following by reducing them to quadratic form:
`sqrt(x^2 - 16) - (x - 4) = sqrt(x^2 - 5x + 4)`.
In each of the following determine whether the given values are solutions of the equation or not
2x2 - 6x + 3 = 0; x = `(1)/(2)`
In each of the following determine whether the given values are solutions of the equation or not.
6x2 - x - 2 = 0; x = `-(1)/(2), x = (2)/(3)`
Solve the following equation by factorization
x2– 4x – 12 = 0,when x∈N
Solve the following equation by factorisation :
2x2 + ax – a2= 0
Complete the following activity to solve the given quadratic equation by factorization method.
Activity: x2 + 8x – 20 = 0
x2 + ( __ ) – 2x – 20 = 0
x (x + 10) – ( __ ) (x + 10) = 0
(x + 10) ( ____ ) = 0
x = ___ or x = 2
