Advertisements
Advertisements
प्रश्न
Mohini wishes to fit three rods together in the shape of a right triangle. If the hypotenuse is 2 cm longer than the base and 4 cm longer than the shortest side, find the lengths of the rods.
Advertisements
उत्तर
Let the length of hypotenuse = x cm
then base = (x – 2)cm
and shortest side = x – 4
According to the condition,
(x)2 = (x - 2)2 + (x - 4)2
⇒ x2 = x2 - 4x + 4 + x2 - 8x + 16
⇒ x2 = 2x2 - 12x + 20
⇒ 2x2 - 12x + 20 - x2 = 0
⇒ x2 - 12x + 20 = 0
⇒ x2 - 10x - 2x + 20 = 0
⇒ x(x - 10) -2(x - 10) = 0
⇒ (x - 10)(x - 2) = 0
Either x - 10 = 0,
then x = 10
or
x - 2 = 0,
then x = 2,
but it is not possible as the hypotenuse is the longest side.
∴ Hypotenuse = 10cm
Base = 10 - 2 = 8cm
and shortest side = 10 - 4 = 6cm.
APPEARS IN
संबंधित प्रश्न
Solve the equation `4/x-3=5/(2x+3); xne0,-3/2` for x .
The numerator of a fraction is 3 less than its denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and original fraction is `29/20`. Find the original fraction.
Solve the following quadratic equations by factorization:
`1/x-1/(x-2)=3` , x ≠ 0, 2
Solve x2 – 4x – 12 =0; when x ∈ I
Solve the following quadratic equation for x:
x2 − 4ax − b2 + 4a2 = 0
If the roots of the equations \[\left( a^2 + b^2 \right) x^2 - 2b\left( a + c \right)x + \left( b^2 + c^2 \right) = 0\] are equal, then
Write the number of zeroes in the end of a number whose prime factorization is 22 × 53 × 32 × 17.
Solve the following equation by factorization
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0
Find the roots of the following quadratic equation by the factorisation method:
`21x^2 - 2x + 1/21 = 0`
If x = –2 is the common solution of quadratic equations ax2 + x – 3a = 0 and x2 + bx + b = 0, then find the value of a2b.
