Advertisements
Advertisements
प्रश्न
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
Advertisements
उत्तर
Using Pythagoras Theorem
`"(hypotenuse)"^2 = sqrt("(height)"^2 + "(base)"^2)`
`AC^2 = sqrt(AB^2 + BC^2)`
`(13)^2 =sqrt( (x )^2 + (x - 7)^2)`
169 = x2 + (x - 7)2
169 = x2 + x2 - 14x + 49
2x2 - 14x - 120 = 0
x2 - 7x - 60 = 0
x2 - 12x + 5x - 60 = 0
x(x - 12) + 5(x - 12) = 0
(x - 12)(x + 5) = 0
Either x - 12 = 0 or x + 5 = 0
x = 12 or x = - 5
Since
Base of right angled triangle = x cm = 12 cm
Right triangle height = x – 7 cm
= 12 - 7
= 5 cm
APPEARS IN
संबंधित प्रश्न
Solve for x
:`1/((x-1)(x-2))+1/((x-2)(x-3))=2/3` , x ≠ 1,2,3
Solve for x :
`3/(x+1)+4/(x-1)=29/(4x-1);x!=1,-1,1/4`
A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. We would like to find out the number of toys produced on that day.
Find the consecutive numbers whose squares have the sum 85.
Find the two consecutive natural numbers whose product is 20.
Solve the following quadratic equations by factorization:
`4(2x – 3)^2 – (2x – 3) – 14 = 0`
If the quadratic equation (c2 – ab) x2 – 2 (a2 – bc) x + b2 – ac = 0 in x, has equal roots, then show that either a = 0 or a3 + b3 + c3 = 3abc ?
Find the value of k for which the following equations have real and equal roots:
\[\left( k + 1 \right) x^2 - 2\left( k - 1 \right)x + 1 = 0\]
Solve the following equation : 5x2 - 11x + 2 = 0
Solve the following equation: 4x2 + 4 bx - (a2 - b2) = 0
Solve the following equation: `("a+b")^2 "x"^2 - 4 "abx" - ("a - b")^2 = 0`
The perimeter of the right angled triangle is 60cm. Its hypotenuse is 25cm. Find the area of the triangle.
The sum of the squares of three consecutive natural numbers is 110. Determine the numbers.
Solve the following equation by factorization
4x2 = 3x
Solve the following equation by factorization
`(2)/(3)x^2 - (1)/(3)x` = 1
Solve the following equation by factorization
2x2 – 9x + 10 = 0,when x∈N
Solve the following equation by factorization
x2 – (p + q)x + pq = 0
If the product of two positive consecutive even integers is 288, find the integers.
The age of a man is twice the square of the age of his son. Eight years hence, the age of the man will be 4 years more than three times the age of his son. Find the present age.
Solve the following equation by factorisation :
3x2 + 11x + 10 = 0
