Advertisements
Advertisements
प्रश्न
The area of right-angled triangle is 600cm2. If the base of the triangle exceeds the altitude by 10cm, find the dimensions of the triangle.
Advertisements
उत्तर
Area of a triangle = `("Height" xx "Base")/2`
Here, Height and base are x and (x + 10 ) and the area is 600
Hence , `x xx (x + 10) xx 1/2 = 600`
⇒ x2 + 10x= 1200
⇒ x2 + 10 x - 1200 = 0
⇒ x2 + 40x - 30 x - 1200 = 0
⇒ x (x + 40} - 30(x + 40) = 0
⇒ (x + 40)(x - 30) = 0, hence x = 30 .
Base = 30+ 10 = 40 cms.
Hence h2= 402 + 302 = 2500
APPEARS IN
संबंधित प्रश्न
In the following determine the set of values of k for which the given quadratic equation has real roots: \[2 x^2 + x + k = 0\]
If \[x^2 + k\left( 4x + k - 1 \right) + 2 = 0\] has equal roots, then k =
Solve the following equation: `"a"/("x" - "a") + "b"/("x" - "b") = (2"c")/("x" - "c")`
Solve the following quadratic equation by factorization method : `"x"^2 - 5"x" - 36 = 0`
The speed of an express train is x km/hr arid the speed of an ordinary train is 12 km/hr less than that of the express train. If the ordinary train takes one hour longer than the express train to cover a distance of 240 km, find the speed of the express train.
Solve the following quadratic equation:
4x2 - 4ax + (a2 - b2) = 0 where a , b ∈ R.
In each of the following determine whether the given values are solutions of the equation or not.
x2 + 6x + 5 = 0; x = -1, x = -5
Solve the following equation by factorization
`(x^2 - 5x)/(2)` = 0
Two squares have sides A cm and (x + 4) cm. The sum of their areas is 656 sq. cm.Express this as an algebraic equation and solve it to find the sides of the squares.
The polynomial equation x(x + 1) + 8 = (x + 2) (x – 2) is:
